Illustrative Math-Media4Math Alignment

 

 

Illustrative Math Alignment: Grade 8 Unit 3

Linear Relationships

Lesson 1: Understanding Proportional Relationships

Use the following Media4Math resources with this Illustrative Math lesson.

Thumbnail Image Title Body Curriculum Topic
Math Example--Coordinate Geometry--Slope Formula: Example 6 Math Example--Coordinate Geometry--Slope Formula: Example 6 Math Example--Coordinate Geometry--Slope Formula: Example 6

Topic

Slope Formula

Description

This example illustrates the calculation of slope for a line connecting two points in different quadrants: (-4, 8) in Quadrant II and (6, 2) in Quadrant I. Applying the slope formula, we find that the slope is (8 - 2) / (-4 - 6) = 6 / -10 = -3 / 5.

The slope formula is a fundamental concept in coordinate geometry, helping us understand the steepness and direction of lines. This example demonstrates how to handle points in different quadrants and interpret a negative slope.

Slope
Math Example--Coordinate Geometry--Slope Formula: Example 6 Math Example--Coordinate Geometry--Slope Formula: Example 6 Math Example--Coordinate Geometry--Slope Formula: Example 6

Topic

Slope Formula

Description

This example illustrates the calculation of slope for a line connecting two points in different quadrants: (-4, 8) in Quadrant II and (6, 2) in Quadrant I. Applying the slope formula, we find that the slope is (8 - 2) / (-4 - 6) = 6 / -10 = -3 / 5.

The slope formula is a fundamental concept in coordinate geometry, helping us understand the steepness and direction of lines. This example demonstrates how to handle points in different quadrants and interpret a negative slope.

Slope
Math Example--Coordinate Geometry--Slope Formula: Example 7 Math Example--Coordinate Geometry--Slope Formula: Example 7 Math Example--Coordinate Geometry--Slope Formula: Example 7

Topic

Slope Formula

Description

This example demonstrates the calculation of slope for a horizontal line connecting two points: (-4, 3) in Quadrant II and (2, 3) in Quadrant I. When we apply the slope formula, we find that the slope is (3 - 3) / (-4 - 2) = 0 / -6 = 0.

The slope formula is a key concept in coordinate geometry, helping us understand the steepness and direction of lines. This particular example highlights a special case where the line is horizontal, resulting in a slope of zero, even when the points are in different quadrants.

Slope
Math Example--Coordinate Geometry--Slope Formula: Example 7 Math Example--Coordinate Geometry--Slope Formula: Example 7 Math Example--Coordinate Geometry--Slope Formula: Example 7

Topic

Slope Formula

Description

This example demonstrates the calculation of slope for a horizontal line connecting two points: (-4, 3) in Quadrant II and (2, 3) in Quadrant I. When we apply the slope formula, we find that the slope is (3 - 3) / (-4 - 2) = 0 / -6 = 0.

The slope formula is a key concept in coordinate geometry, helping us understand the steepness and direction of lines. This particular example highlights a special case where the line is horizontal, resulting in a slope of zero, even when the points are in different quadrants.

Slope
Math Example--Coordinate Geometry--Slope Formula: Example 7 Math Example--Coordinate Geometry--Slope Formula: Example 7 Math Example--Coordinate Geometry--Slope Formula: Example 7

Topic

Slope Formula

Description

This example demonstrates the calculation of slope for a horizontal line connecting two points: (-4, 3) in Quadrant II and (2, 3) in Quadrant I. When we apply the slope formula, we find that the slope is (3 - 3) / (-4 - 2) = 0 / -6 = 0.

The slope formula is a key concept in coordinate geometry, helping us understand the steepness and direction of lines. This particular example highlights a special case where the line is horizontal, resulting in a slope of zero, even when the points are in different quadrants.

Slope
Math Example--Coordinate Geometry--Slope Formula: Example 8 Math Example--Coordinate Geometry--Slope Formula: Example 8 Math Example--Coordinate Geometry--Slope Formula: Example 8

Topic

Slope Formula

Description

This example illustrates the calculation of slope for a line connecting two points in different quadrants: (-2, -8) in Quadrant III and (6, 2) in Quadrant I. Applying the slope formula, we find that the slope is (2 - (-8)) / (6 - (-2)) = 10 / 8 = 5 / 4.

The slope formula is a crucial concept in coordinate geometry, helping us understand the steepness and direction of lines. This example shows how to handle negative coordinates and points in different quadrants when calculating slope.

Slope
Math Example--Coordinate Geometry--Slope Formula: Example 8 Math Example--Coordinate Geometry--Slope Formula: Example 8 Math Example--Coordinate Geometry--Slope Formula: Example 8

Topic

Slope Formula

Description

This example illustrates the calculation of slope for a line connecting two points in different quadrants: (-2, -8) in Quadrant III and (6, 2) in Quadrant I. Applying the slope formula, we find that the slope is (2 - (-8)) / (6 - (-2)) = 10 / 8 = 5 / 4.

The slope formula is a crucial concept in coordinate geometry, helping us understand the steepness and direction of lines. This example shows how to handle negative coordinates and points in different quadrants when calculating slope.

Slope
Math Example--Coordinate Geometry--Slope Formula: Example 8 Math Example--Coordinate Geometry--Slope Formula: Example 8 Math Example--Coordinate Geometry--Slope Formula: Example 8

Topic

Slope Formula

Description

This example illustrates the calculation of slope for a line connecting two points in different quadrants: (-2, -8) in Quadrant III and (6, 2) in Quadrant I. Applying the slope formula, we find that the slope is (2 - (-8)) / (6 - (-2)) = 10 / 8 = 5 / 4.

The slope formula is a crucial concept in coordinate geometry, helping us understand the steepness and direction of lines. This example shows how to handle negative coordinates and points in different quadrants when calculating slope.

Slope
Math Example--Coordinate Geometry--Slope Formula: Example 9 Math Example--Coordinate Geometry--Slope Formula: Example 9 Math Example--Coordinate Geometry--Slope Formula: Example 9

Topic

Slope Formula

Description

This example demonstrates the calculation of slope for a line connecting two points: (9, 6) and (2, -8) on a Cartesian plane. Applying the slope formula, we find that the slope is (6 - (-8)) / (9 - 2) = 14 / 7 = 2.

The slope formula is a fundamental concept in coordinate geometry, helping us understand the steepness and direction of lines. This example shows how to handle points with both positive and negative coordinates when calculating slope.

Slope
Math Example--Coordinate Geometry--Slope Formula: Example 9 Math Example--Coordinate Geometry--Slope Formula: Example 9 Math Example--Coordinate Geometry--Slope Formula: Example 9

Topic

Slope Formula

Description

This example demonstrates the calculation of slope for a line connecting two points: (9, 6) and (2, -8) on a Cartesian plane. Applying the slope formula, we find that the slope is (6 - (-8)) / (9 - 2) = 14 / 7 = 2.

The slope formula is a fundamental concept in coordinate geometry, helping us understand the steepness and direction of lines. This example shows how to handle points with both positive and negative coordinates when calculating slope.

Slope
Math Example--Coordinate Geometry--Slope Formula: Example 9 Math Example--Coordinate Geometry--Slope Formula: Example 9 Math Example--Coordinate Geometry--Slope Formula: Example 9

Topic

Slope Formula

Description

This example demonstrates the calculation of slope for a line connecting two points: (9, 6) and (2, -8) on a Cartesian plane. Applying the slope formula, we find that the slope is (6 - (-8)) / (9 - 2) = 14 / 7 = 2.

The slope formula is a fundamental concept in coordinate geometry, helping us understand the steepness and direction of lines. This example shows how to handle points with both positive and negative coordinates when calculating slope.

Slope
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 1 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 1 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 1

Topic

Linear Functions

Description

This example demonstrates how to find the equation of a line passing through two given points: (6, 4) and (8, 8). The slope is calculated using the formula (y2 - y1) / (x2 - x1), resulting in a slope of 2. Using the point-slope form of a line, y - y1 = m(x - x1), the equation is derived as y - 8 = 2(x - 8), which simplifies to y = 2x - 8.

Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 1 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 1 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 1

Topic

Linear Functions

Description

This example demonstrates how to find the equation of a line passing through two given points: (6, 4) and (8, 8). The slope is calculated using the formula (y2 - y1) / (x2 - x1), resulting in a slope of 2. Using the point-slope form of a line, y - y1 = m(x - x1), the equation is derived as y - 8 = 2(x - 8), which simplifies to y = 2x - 8.

Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 1 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 1 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 1

Topic

Linear Functions

Description

This example demonstrates how to find the equation of a line passing through two given points: (6, 4) and (8, 8). The slope is calculated using the formula (y2 - y1) / (x2 - x1), resulting in a slope of 2. Using the point-slope form of a line, y - y1 = m(x - x1), the equation is derived as y - 8 = 2(x - 8), which simplifies to y = 2x - 8.

Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 10 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 10 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 10

Topic

Linear Functions

Description

The image shows a coordinate plane with two points (-6, -2) and (-2, -6) marked. It provides a step-by-step solution to find the equation of the line passing through these points. The slope is calculated, and the equation is derived using point-slope form. The slope is calculated as (y2 - y1) / (x2 - x1) = (-6 - (-2)) / (-2 - (-6)) = -4 / 4 = -1. Using point-slope form, y - y1 = m(x - x1), the equation is derived as y + 2 = -(x + 6), which simplifies to y = -x - 8.

Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 10 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 10 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 10

Topic

Linear Functions

Description

The image shows a coordinate plane with two points (-6, -2) and (-2, -6) marked. It provides a step-by-step solution to find the equation of the line passing through these points. The slope is calculated, and the equation is derived using point-slope form. The slope is calculated as (y2 - y1) / (x2 - x1) = (-6 - (-2)) / (-2 - (-6)) = -4 / 4 = -1. Using point-slope form, y - y1 = m(x - x1), the equation is derived as y + 2 = -(x + 6), which simplifies to y = -x - 8.

Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 10 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 10 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 10

Topic

Linear Functions

Description

The image shows a coordinate plane with two points (-6, -2) and (-2, -6) marked. It provides a step-by-step solution to find the equation of the line passing through these points. The slope is calculated, and the equation is derived using point-slope form. The slope is calculated as (y2 - y1) / (x2 - x1) = (-6 - (-2)) / (-2 - (-6)) = -4 / 4 = -1. Using point-slope form, y - y1 = m(x - x1), the equation is derived as y + 2 = -(x + 6), which simplifies to y = -x - 8.

Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 11 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 11 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 11

Topic

Linear Functions

Description

The image shows a coordinate plane with two points (-8, -4) and (-2, -4) marked. It provides a step-by-step solution to find the equation of the line passing through these points. The slope is calculated as zero, indicating a horizontal line. The slope is calculated as (y2 - y1) / (x2 - x1) = (-4 - (-4)) / (-8 - (-2)) = 0 / -6 = 0. Since the slope is zero, it indicates a horizontal line at y = -4. Using point-slope form, the equation becomes y + 4 = 0, which simplifies to y = -4.

Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 11 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 11 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 11

Topic

Linear Functions

Description

The image shows a coordinate plane with two points (-8, -4) and (-2, -4) marked. It provides a step-by-step solution to find the equation of the line passing through these points. The slope is calculated as zero, indicating a horizontal line. The slope is calculated as (y2 - y1) / (x2 - x1) = (-4 - (-4)) / (-8 - (-2)) = 0 / -6 = 0. Since the slope is zero, it indicates a horizontal line at y = -4. Using point-slope form, the equation becomes y + 4 = 0, which simplifies to y = -4.

Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 11 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 11 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 11

Topic

Linear Functions

Description

The image shows a coordinate plane with two points (-8, -4) and (-2, -4) marked. It provides a step-by-step solution to find the equation of the line passing through these points. The slope is calculated as zero, indicating a horizontal line. The slope is calculated as (y2 - y1) / (x2 - x1) = (-4 - (-4)) / (-8 - (-2)) = 0 / -6 = 0. Since the slope is zero, it indicates a horizontal line at y = -4. Using point-slope form, the equation becomes y + 4 = 0, which simplifies to y = -4.

Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 12 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 12 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 12

Topic

Linear Functions

Description

The image shows a coordinate plane with two points (-5, -8) and (-5, -3) marked. It provides a step-by-step solution to find the equation of the line passing through these points. The slope is undefined, indicating a vertical line. The slope is calculated as (y2 - y1) / (x2 - x1) = (-3 - (-8)) / (-5 - (-5)) = 5 / 0, which is undefined. Since the slope is undefined, it indicates a vertical line at x = -5. Therefore, the equation of the line is simply x = -5.

Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 12 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 12 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 12

Topic

Linear Functions

Description

The image shows a coordinate plane with two points (-5, -8) and (-5, -3) marked. It provides a step-by-step solution to find the equation of the line passing through these points. The slope is undefined, indicating a vertical line. The slope is calculated as (y2 - y1) / (x2 - x1) = (-3 - (-8)) / (-5 - (-5)) = 5 / 0, which is undefined. Since the slope is undefined, it indicates a vertical line at x = -5. Therefore, the equation of the line is simply x = -5.

Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 12 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 12 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 12

Topic

Linear Functions

Description

The image shows a coordinate plane with two points (-5, -8) and (-5, -3) marked. It provides a step-by-step solution to find the equation of the line passing through these points. The slope is undefined, indicating a vertical line. The slope is calculated as (y2 - y1) / (x2 - x1) = (-3 - (-8)) / (-5 - (-5)) = 5 / 0, which is undefined. Since the slope is undefined, it indicates a vertical line at x = -5. Therefore, the equation of the line is simply x = -5.

Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 13 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 13 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 13

Topic

Linear Functions

Description

This image shows a graph with two points (2, -4) and (6, -2) marked. The example demonstrates how to find the equation of a line passing through these points. The slope is calculated as 1/2, and the point-slope form is used to derive the equation of the line. The slope formula is used: (y2 - y1) / (x2 - x1) = (-2 - (-4)) / (6 - 2) = 2 / 4 = 1/2. Then, using the point-slope form: y - (-2) = (1/2)(x - 6), which simplifies to y = (1/2)x - 5.

Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 13 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 13 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 13

Topic

Linear Functions

Description

This image shows a graph with two points (2, -4) and (6, -2) marked. The example demonstrates how to find the equation of a line passing through these points. The slope is calculated as 1/2, and the point-slope form is used to derive the equation of the line. The slope formula is used: (y2 - y1) / (x2 - x1) = (-2 - (-4)) / (6 - 2) = 2 / 4 = 1/2. Then, using the point-slope form: y - (-2) = (1/2)(x - 6), which simplifies to y = (1/2)x - 5.

Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 13 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 13 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 13

Topic

Linear Functions

Description

This image shows a graph with two points (2, -4) and (6, -2) marked. The example demonstrates how to find the equation of a line passing through these points. The slope is calculated as 1/2, and the point-slope form is used to derive the equation of the line. The slope formula is used: (y2 - y1) / (x2 - x1) = (-2 - (-4)) / (6 - 2) = 2 / 4 = 1/2. Then, using the point-slope form: y - (-2) = (1/2)(x - 6), which simplifies to y = (1/2)x - 5.

Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 14 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 14 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 14

Topic

Linear Functions

Description

This image shows a graph with two points (2, -3) and (5, -6). The example demonstrates how to find the equation of a line passing through these points. The slope is calculated as -1, and the point-slope form is used to derive the equation. The slope formula is used: (y2 - y1) / (x2 - x1) = (-3 - (-6)) / (2 - 5) = 3 / -3 = -1. Then, using the point-slope form: y - (-3) = -(x - 2), which simplifies to y = -x - 1.

Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 14 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 14 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 14

Topic

Linear Functions

Description

This image shows a graph with two points (2, -3) and (5, -6). The example demonstrates how to find the equation of a line passing through these points. The slope is calculated as -1, and the point-slope form is used to derive the equation. The slope formula is used: (y2 - y1) / (x2 - x1) = (-3 - (-6)) / (2 - 5) = 3 / -3 = -1. Then, using the point-slope form: y - (-3) = -(x - 2), which simplifies to y = -x - 1.

Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 14 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 14 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 14

Topic

Linear Functions

Description

This image shows a graph with two points (2, -3) and (5, -6). The example demonstrates how to find the equation of a line passing through these points. The slope is calculated as -1, and the point-slope form is used to derive the equation. The slope formula is used: (y2 - y1) / (x2 - x1) = (-3 - (-6)) / (2 - 5) = 3 / -3 = -1. Then, using the point-slope form: y - (-3) = -(x - 2), which simplifies to y = -x - 1.

Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 15 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 15 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 15

Topic

Linear Functions

Description

This image shows a graph with two points (3, -4) and (7, -4). The example demonstrates how to find the equation of a horizontal line passing through these points. The slope is calculated as 0, and the point-slope form is used to derive the equation. The slope formula is used: (y2 - y1) / (x2 - x1) = (-4 - (-4)) / (7 - 3) = 0 / 4 = 0. Then, using the point-slope form: y - (-4) = 0(x - 3), which simplifies to y = -4.

Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 15 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 15 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 15

Topic

Linear Functions

Description

This image shows a graph with two points (3, -4) and (7, -4). The example demonstrates how to find the equation of a horizontal line passing through these points. The slope is calculated as 0, and the point-slope form is used to derive the equation. The slope formula is used: (y2 - y1) / (x2 - x1) = (-4 - (-4)) / (7 - 3) = 0 / 4 = 0. Then, using the point-slope form: y - (-4) = 0(x - 3), which simplifies to y = -4.

Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 15 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 15 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 15

Topic

Linear Functions

Description

This image shows a graph with two points (3, -4) and (7, -4). The example demonstrates how to find the equation of a horizontal line passing through these points. The slope is calculated as 0, and the point-slope form is used to derive the equation. The slope formula is used: (y2 - y1) / (x2 - x1) = (-4 - (-4)) / (7 - 3) = 0 / 4 = 0. Then, using the point-slope form: y - (-4) = 0(x - 3), which simplifies to y = -4.

Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 16 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 16 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 16

Topic

Linear Functions

Description

This image shows a graph with two points (4, -8) and (4, -2). The example demonstrates how to find the equation of a vertical line passing through these points. The slope is undefined because division by zero occurs in calculating it. The slope formula is used: (y2 - y1) / (x2 - x1) = (-2 - (-8)) / (4 - 4) = 6 / 0 = undefined. Since this represents a vertical line, its equation is simply x = 4.

Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 16 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 16 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 16

Topic

Linear Functions

Description

This image shows a graph with two points (4, -8) and (4, -2). The example demonstrates how to find the equation of a vertical line passing through these points. The slope is undefined because division by zero occurs in calculating it. The slope formula is used: (y2 - y1) / (x2 - x1) = (-2 - (-8)) / (4 - 4) = 6 / 0 = undefined. Since this represents a vertical line, its equation is simply x = 4.

Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 16 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 16 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 16

Topic

Linear Functions

Description

This image shows a graph with two points (4, -8) and (4, -2). The example demonstrates how to find the equation of a vertical line passing through these points. The slope is undefined because division by zero occurs in calculating it. The slope formula is used: (y2 - y1) / (x2 - x1) = (-2 - (-8)) / (4 - 4) = 6 / 0 = undefined. Since this represents a vertical line, its equation is simply x = 4.

Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 17 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 17 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 17

Topic

Linear Functions

Description

This image shows a graph with two points plotted at (-2, 0.5) and (5, 4). The example demonstrates how to find the equation of a line using the slope formula and point-slope form. The slope is calculated as (4 - 0.5) / (5 - (-2)) = 3.5 / 7 = 1 / 2. The point-slope form is used to find the equation: y - 4 = (1 / 2)(x - 5), resulting in y = (1 / 2)x + 1 / 2.

Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 17 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 17 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 17

Topic

Linear Functions

Description

This image shows a graph with two points plotted at (-2, 0.5) and (5, 4). The example demonstrates how to find the equation of a line using the slope formula and point-slope form. The slope is calculated as (4 - 0.5) / (5 - (-2)) = 3.5 / 7 = 1 / 2. The point-slope form is used to find the equation: y - 4 = (1 / 2)(x - 5), resulting in y = (1 / 2)x + 1 / 2.

Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 17 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 17 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 17

Topic

Linear Functions

Description

This image shows a graph with two points plotted at (-2, 0.5) and (5, 4). The example demonstrates how to find the equation of a line using the slope formula and point-slope form. The slope is calculated as (4 - 0.5) / (5 - (-2)) = 3.5 / 7 = 1 / 2. The point-slope form is used to find the equation: y - 4 = (1 / 2)(x - 5), resulting in y = (1 / 2)x + 1 / 2.

Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 18 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 18 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 18

Topic

Linear Functions

Description

This image shows a graph with two points plotted at (-3, 5) and (5, 1). The example demonstrates how to find the equation of a line using the slope formula and point-slope form. The slope is calculated as (5 - 1) / (-3 - 5) = -1 / 2. The point-slope form is used to find the equation: y - 5 = (-1 / 2)(x + 3), resulting in y = (-1 / 2)x + 7 / 2.

Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 18 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 18 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 18

Topic

Linear Functions

Description

This image shows a graph with two points plotted at (-3, 5) and (5, 1). The example demonstrates how to find the equation of a line using the slope formula and point-slope form. The slope is calculated as (5 - 1) / (-3 - 5) = -1 / 2. The point-slope form is used to find the equation: y - 5 = (-1 / 2)(x + 3), resulting in y = (-1 / 2)x + 7 / 2.

Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 18 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 18 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 18

Topic

Linear Functions

Description

This image shows a graph with two points plotted at (-3, 5) and (5, 1). The example demonstrates how to find the equation of a line using the slope formula and point-slope form. The slope is calculated as (5 - 1) / (-3 - 5) = -1 / 2. The point-slope form is used to find the equation: y - 5 = (-1 / 2)(x + 3), resulting in y = (-1 / 2)x + 7 / 2.

Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 19 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 19 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 19

Topic

Linear Functions

Description

This image shows a graph with two points plotted at (-4, 3) and (6, 3). The example demonstrates how to find the equation of a horizontal line using the slope formula and point-slope form. The slope is calculated as (3 - 3) / (-4 - 6) = 0. Since the slope is zero, the equation of the line is simply y = 3, indicating a horizontal line passing through y = 3.

Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 19 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 19 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 19

Topic

Linear Functions

Description

This image shows a graph with two points plotted at (-4, 3) and (6, 3). The example demonstrates how to find the equation of a horizontal line using the slope formula and point-slope form. The slope is calculated as (3 - 3) / (-4 - 6) = 0. Since the slope is zero, the equation of the line is simply y = 3, indicating a horizontal line passing through y = 3.

Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 19 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 19 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 19

Topic

Linear Functions

Description

This image shows a graph with two points plotted at (-4, 3) and (6, 3). The example demonstrates how to find the equation of a horizontal line using the slope formula and point-slope form. The slope is calculated as (3 - 3) / (-4 - 6) = 0. Since the slope is zero, the equation of the line is simply y = 3, indicating a horizontal line passing through y = 3.

Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 2 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 2 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 2

Topic

Linear Functions

Description

This example illustrates the process of finding the equation of a line passing through the points (3, 7) and (9, 1). The slope is calculated as -1 using the formula (y2 - y1) / (x2 - x1). Employing the point-slope form, y - y1 = m(x - x1), the equation is derived as y - 1 = -(x - 9), which simplifies to y = -x + 10.

Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 2 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 2 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 2

Topic

Linear Functions

Description

This example illustrates the process of finding the equation of a line passing through the points (3, 7) and (9, 1). The slope is calculated as -1 using the formula (y2 - y1) / (x2 - x1). Employing the point-slope form, y - y1 = m(x - x1), the equation is derived as y - 1 = -(x - 9), which simplifies to y = -x + 10.

Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 2 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 2 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 2

Topic

Linear Functions

Description

This example illustrates the process of finding the equation of a line passing through the points (3, 7) and (9, 1). The slope is calculated as -1 using the formula (y2 - y1) / (x2 - x1). Employing the point-slope form, y - y1 = m(x - x1), the equation is derived as y - 1 = -(x - 9), which simplifies to y = -x + 10.

Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 20 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 20 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 20

Topic

Linear Functions

Description

This image shows a graph with two points plotted at (-3, -5) and (5, 1). The example demonstrates how to find the equation of a line using the slope formula and point-slope form. The slope is calculated as (1 - (-5)) / (5 - (-3)) = 6 / 8 = 3 / 4. The point-slope form is used to find the equation: y - 1 = (3 / 4)(x - 5), resulting in y = 3/4x - 2 3/4.

Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 20 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 20 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 20

Topic

Linear Functions

Description

This image shows a graph with two points plotted at (-3, -5) and (5, 1). The example demonstrates how to find the equation of a line using the slope formula and point-slope form. The slope is calculated as (1 - (-5)) / (5 - (-3)) = 6 / 8 = 3 / 4. The point-slope form is used to find the equation: y - 1 = (3 / 4)(x - 5), resulting in y = 3/4x - 2 3/4.

Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 20 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 20 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 20

Topic

Linear Functions

Description

This image shows a graph with two points plotted at (-3, -5) and (5, 1). The example demonstrates how to find the equation of a line using the slope formula and point-slope form. The slope is calculated as (1 - (-5)) / (5 - (-3)) = 6 / 8 = 3 / 4. The point-slope form is used to find the equation: y - 1 = (3 / 4)(x - 5), resulting in y = 3/4x - 2 3/4.

Point-Slope Form and Slope-Intercept Form