Illustrative Math-Media4Math Alignment

 

 

Illustrative Math Alignment: Grade 8 Unit 3

Linear Relationships

Lesson 10: Calculating Slope

Use the following Media4Math resources with this Illustrative Math lesson.

Thumbnail Image Title Body Curriculum Topic
Math Example--Coordinate Geometry--Slope Formula: Example 10 Math Example--Coordinate Geometry--Slope Formula: Example 10 Math Example--Coordinate Geometry--Slope Formula: Example 10

Topic

Slope Formula

Description

This example illustrates the calculation of slope for a line connecting two points: (1, 6) and (10, -3) on a Cartesian plane. Applying the slope formula, we find that the slope is (6 - (-3)) / (1 - 10) = 9 / -9 = -1.

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

Slope
Math Example--Coordinate Geometry--Slope Formula: Example 11 Math Example--Coordinate Geometry--Slope Formula: Example 11 Math Example--Coordinate Geometry--Slope Formula: Example 11

Topic

Slope Formula

Description

This example demonstrates the calculation of slope for a vertical line connecting points (5, 6) and (5, -8) on a Cartesian plane. When we apply the slope formula, we find that the slope is (6 - (-8)) / (5 - 5) = 14 / 0, which is undefined.

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 vertical, resulting in an undefined slope.

Slope
Math Example--Coordinate Geometry--Slope Formula: Example 11 Math Example--Coordinate Geometry--Slope Formula: Example 11 Math Example--Coordinate Geometry--Slope Formula: Example 11

Topic

Slope Formula

Description

This example demonstrates the calculation of slope for a vertical line connecting points (5, 6) and (5, -8) on a Cartesian plane. When we apply the slope formula, we find that the slope is (6 - (-8)) / (5 - 5) = 14 / 0, which is undefined.

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 vertical, resulting in an undefined slope.

Slope
Math Example--Coordinate Geometry--Slope Formula: Example 12 Math Example--Coordinate Geometry--Slope Formula: Example 12 Math Example--Coordinate Geometry--Slope Formula: Example 12

Topic

Slope Formula

Description

This example illustrates the calculation of slope for a line connecting two points: (-2, 6) and (-4, -8) on a Cartesian plane. Applying the slope formula, we find that the slope is (6 - (-8)) / (-2 - (-4)) = 14 / 2 = 7.

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 with negative coordinates when calculating slope, resulting in a positive slope.

Slope
Math Example--Coordinate Geometry--Slope Formula: Example 12 Math Example--Coordinate Geometry--Slope Formula: Example 12 Math Example--Coordinate Geometry--Slope Formula: Example 12

Topic

Slope Formula

Description

This example illustrates the calculation of slope for a line connecting two points: (-2, 6) and (-4, -8) on a Cartesian plane. Applying the slope formula, we find that the slope is (6 - (-8)) / (-2 - (-4)) = 14 / 2 = 7.

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 with negative coordinates when calculating slope, resulting in a positive slope.

Slope
Math Example--Coordinate Geometry--Slope Formula: Example 13 Math Example--Coordinate Geometry--Slope Formula: Example 13 Math Example--Coordinate Geometry--Slope Formula: Example 13

Topic

Slope Formula

Description

This example demonstrates the calculation of slope for a line connecting two points: (-10, 6) and (-1, -1) on a Cartesian plane. The line crosses quadrants II and III. Applying the slope formula, we find that the slope is (6 - (-1)) / (-10 - (-1)) = 7 / -9 = -7 / 9.

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 points in different quadrants and with negative coordinates when calculating slope.

Slope
Math Example--Coordinate Geometry--Slope Formula: Example 13 Math Example--Coordinate Geometry--Slope Formula: Example 13 Math Example--Coordinate Geometry--Slope Formula: Example 13

Topic

Slope Formula

Description

This example demonstrates the calculation of slope for a line connecting two points: (-10, 6) and (-1, -1) on a Cartesian plane. The line crosses quadrants II and III. Applying the slope formula, we find that the slope is (6 - (-1)) / (-10 - (-1)) = 7 / -9 = -7 / 9.

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 points in different quadrants and with negative coordinates when calculating slope.

Slope
Math Example--Coordinate Geometry--Slope Formula: Example 14 Math Example--Coordinate Geometry--Slope Formula: Example 14 Math Example--Coordinate Geometry--Slope Formula: Example 14

Topic

Slope Formula

Description

This example illustrates the calculation of slope for a vertical line passing through two points: (-5, 6) and (-5, -4) in Quadrant II of a Cartesian plane. When we apply the slope formula, we find that the slope is (6 - (-4)) / (-5 - (-5)) = 10 / 0, which is undefined.

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 vertical, resulting in an undefined slope.

Slope
Math Example--Coordinate Geometry--Slope Formula: Example 14 Math Example--Coordinate Geometry--Slope Formula: Example 14 Math Example--Coordinate Geometry--Slope Formula: Example 14

Topic

Slope Formula

Description

This example illustrates the calculation of slope for a vertical line passing through two points: (-5, 6) and (-5, -4) in Quadrant II of a Cartesian plane. When we apply the slope formula, we find that the slope is (6 - (-4)) / (-5 - (-5)) = 10 / 0, which is undefined.

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 vertical, resulting in an undefined slope.

Slope
Math Example--Coordinate Geometry--Slope Formula: Example 15 Math Example--Coordinate Geometry--Slope Formula: Example 15 Math Example--Coordinate Geometry--Slope Formula: Example 15

Topic

Slope Formula

Description

This example demonstrates the calculation of slope for a line connecting two points: (4, -5) and (-2, -7) on a Cartesian plane. The line crosses quadrants III and IV. Applying the slope formula, we find that the slope is (-5 - (-7)) / (4 - (-2)) = 2 / 6 = 1 / 3.

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 negative coordinates and in different quadrants when calculating slope.

Slope
Math Example--Coordinate Geometry--Slope Formula: Example 15 Math Example--Coordinate Geometry--Slope Formula: Example 15 Math Example--Coordinate Geometry--Slope Formula: Example 15

Topic

Slope Formula

Description

This example demonstrates the calculation of slope for a line connecting two points: (4, -5) and (-2, -7) on a Cartesian plane. The line crosses quadrants III and IV. Applying the slope formula, we find that the slope is (-5 - (-7)) / (4 - (-2)) = 2 / 6 = 1 / 3.

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 negative coordinates and in different quadrants when calculating slope.

Slope
Math Example--Coordinate Geometry--Slope Formula: Example 16 Math Example--Coordinate Geometry--Slope Formula: Example 16 Math Example--Coordinate Geometry--Slope Formula: Example 16

Topic

Slope Formula

Description

This example demonstrates the calculation of slope for a line connecting two points: (9, -10) and (-1, -2) on a Cartesian plane. The line crosses quadrants III and IV diagonally. Applying the slope formula, we find that the slope is (-2 - (-10)) / (-1 - 9) = 8 / -10 = -4 / 5.

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, resulting in a negative fraction.

Slope
Math Example--Coordinate Geometry--Slope Formula: Example 16 Math Example--Coordinate Geometry--Slope Formula: Example 16 Math Example--Coordinate Geometry--Slope Formula: Example 16

Topic

Slope Formula

Description

This example demonstrates the calculation of slope for a line connecting two points: (9, -10) and (-1, -2) on a Cartesian plane. The line crosses quadrants III and IV diagonally. Applying the slope formula, we find that the slope is (-2 - (-10)) / (-1 - 9) = 8 / -10 = -4 / 5.

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, resulting in a negative fraction.

Slope
Math Example--Coordinate Geometry--Slope Formula: Example 17 Math Example--Coordinate Geometry--Slope Formula: Example 17 Math Example--Coordinate Geometry--Slope Formula: Example 17

Topic

Slope Formula

Description

This example illustrates the calculation of slope for a horizontal line connecting points (-2, -7) and (3, -7) on a Cartesian plane. When we apply the slope formula, we find that the slope is (-7 - (-7)) / (-2 - 3) = 0 / -5 = 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 have different x-coordinates.

Slope
Math Example--Coordinate Geometry--Slope Formula: Example 17 Math Example--Coordinate Geometry--Slope Formula: Example 17 Math Example--Coordinate Geometry--Slope Formula: Example 17

Topic

Slope Formula

Description

This example illustrates the calculation of slope for a horizontal line connecting points (-2, -7) and (3, -7) on a Cartesian plane. When we apply the slope formula, we find that the slope is (-7 - (-7)) / (-2 - 3) = 0 / -5 = 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 have different x-coordinates.

Slope
Math Example--Coordinate Geometry--Slope Formula: Example 18 Math Example--Coordinate Geometry--Slope Formula: Example 18 Math Example--Coordinate Geometry--Slope Formula: Example 18

Topic

Slope Formula

Description

This example demonstrates the calculation of slope for a line connecting two points: (-6, 0) and (0, 4) on a Cartesian plane. Applying the slope formula, we find that the slope is (4 - 0) / (0 - (-6)) = 4 / 6 = 2 / 3.

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, resulting in a positive fraction.

Slope
Math Example--Coordinate Geometry--Slope Formula: Example 18 Math Example--Coordinate Geometry--Slope Formula: Example 18 Math Example--Coordinate Geometry--Slope Formula: Example 18

Topic

Slope Formula

Description

This example demonstrates the calculation of slope for a line connecting two points: (-6, 0) and (0, 4) on a Cartesian plane. Applying the slope formula, we find that the slope is (4 - 0) / (0 - (-6)) = 4 / 6 = 2 / 3.

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, resulting in a positive fraction.

Slope
Math Example--Coordinate Geometry--Slope Formula: Example 19 Math Example--Coordinate Geometry--Slope Formula: Example 19 Math Example--Coordinate Geometry--Slope Formula: Example 19

Topic

Slope Formula

Description

This example illustrates the calculation of slope for a line connecting two points: (1, 0) and (0, 6) on a Cartesian plane. Applying the slope formula, we find that the slope is (6 - 0) / (0 - 1) = 6 / -1 = -6.

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

Slope
Math Example--Coordinate Geometry--Slope Formula: Example 19 Math Example--Coordinate Geometry--Slope Formula: Example 19 Math Example--Coordinate Geometry--Slope Formula: Example 19

Topic

Slope Formula

Description

This example illustrates the calculation of slope for a line connecting two points: (1, 0) and (0, 6) on a Cartesian plane. Applying the slope formula, we find that the slope is (6 - 0) / (0 - 1) = 6 / -1 = -6.

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

Slope
Math Example--Coordinate Geometry--Slope Formula: Example 2 Math Example--Coordinate Geometry--Slope Formula: Example 2 Math Example--Coordinate Geometry--Slope Formula: Example 2

Topic

Slope Formula

Description

This example illustrates the calculation of slope between two points (3, 7) and (9, 2) on a coordinate grid. The slope formula is applied to find that the slope is (7 - 2) / (3 - 9) = 5 / -6 = -5 / 6.

Understanding the slope formula is crucial in coordinate geometry as it helps describe the steepness and direction of a line. This concept is widely used in various mathematical applications and real-world scenarios.

Slope
Math Example--Coordinate Geometry--Slope Formula: Example 2 Math Example--Coordinate Geometry--Slope Formula: Example 2 Math Example--Coordinate Geometry--Slope Formula: Example 2

Topic

Slope Formula

Description

This example illustrates the calculation of slope between two points (3, 7) and (9, 2) on a coordinate grid. The slope formula is applied to find that the slope is (7 - 2) / (3 - 9) = 5 / -6 = -5 / 6.

Understanding the slope formula is crucial in coordinate geometry as it helps describe the steepness and direction of a line. This concept is widely used in various mathematical applications and real-world scenarios.

Slope
Math Example--Coordinate Geometry--Slope Formula: Example 20 Math Example--Coordinate Geometry--Slope Formula: Example 20 Math Example--Coordinate Geometry--Slope Formula: Example 20

Topic

Slope Formula

Description

This example demonstrates the calculation of slope for a horizontal line connecting points (0, 0) and (8, 0) on a Cartesian plane. When we apply the slope formula, we find that the slope is (0 - 0) / (8 - 0) = 0 / 8 = 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 and lies on the x-axis, resulting in a slope of zero.

Slope
Math Example--Coordinate Geometry--Slope Formula: Example 20 Math Example--Coordinate Geometry--Slope Formula: Example 20 Math Example--Coordinate Geometry--Slope Formula: Example 20

Topic

Slope Formula

Description

This example demonstrates the calculation of slope for a horizontal line connecting points (0, 0) and (8, 0) on a Cartesian plane. When we apply the slope formula, we find that the slope is (0 - 0) / (8 - 0) = 0 / 8 = 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 and lies on the x-axis, resulting in a slope of zero.

Slope
Math Example--Coordinate Geometry--Slope Formula: Example 21 Math Example--Coordinate Geometry--Slope Formula: Example 21 Math Example--Coordinate Geometry--Slope Formula: Example 21

Topic

Slope Formula

Description

This example illustrates the calculation of slope for a vertical line connecting points (0, 0) and (0, 6) on a Cartesian plane. When we apply the slope formula, we find that the slope is (6 - 0) / (0 - 0) = 6 / 0, which is undefined.

The slope formula is a fundamental concept in coordinate geometry, helping us understand the steepness and direction of lines. This particular example highlights a special case where the line is vertical and lies on the y-axis, resulting in an undefined slope due to division by zero.

Slope
Math Example--Coordinate Geometry--Slope Formula: Example 21 Math Example--Coordinate Geometry--Slope Formula: Example 21 Math Example--Coordinate Geometry--Slope Formula: Example 21

Topic

Slope Formula

Description

This example illustrates the calculation of slope for a vertical line connecting points (0, 0) and (0, 6) on a Cartesian plane. When we apply the slope formula, we find that the slope is (6 - 0) / (0 - 0) = 6 / 0, which is undefined.

The slope formula is a fundamental concept in coordinate geometry, helping us understand the steepness and direction of lines. This particular example highlights a special case where the line is vertical and lies on the y-axis, resulting in an undefined slope due to division by zero.

Slope
Math Example--Coordinate Geometry--Slope Formula: Example 3 Math Example--Coordinate Geometry--Slope Formula: Example 3 Math Example--Coordinate Geometry--Slope Formula: Example 3

Topic

Slope Formula

Description

This example demonstrates the calculation of slope for a horizontal line connecting points (2, 4) and (9, 4) on a coordinate grid. When we apply the slope formula, we find that the slope is (4 - 4) / (9 - 2) = 0 / 7 = 0.

The slope formula is a fundamental 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.

Slope
Math Example--Coordinate Geometry--Slope Formula: Example 3 Math Example--Coordinate Geometry--Slope Formula: Example 3 Math Example--Coordinate Geometry--Slope Formula: Example 3

Topic

Slope Formula

Description

This example demonstrates the calculation of slope for a horizontal line connecting points (2, 4) and (9, 4) on a coordinate grid. When we apply the slope formula, we find that the slope is (4 - 4) / (9 - 2) = 0 / 7 = 0.

The slope formula is a fundamental 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.

Slope
Math Example--Coordinate Geometry--Slope Formula: Example 4 Math Example--Coordinate Geometry--Slope Formula: Example 4 Math Example--Coordinate Geometry--Slope Formula: Example 4

Topic

Slope Formula

Description

This example illustrates the calculation of slope for a vertical line passing through points (5, 8) and (5, 2) on a coordinate grid. When we apply the slope formula, we find that the slope is (8 - 2) / (5 - 5) = 6 / 0, which is undefined.

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 vertical, resulting in an undefined slope.

Slope
Math Example--Coordinate Geometry--Slope Formula: Example 4 Math Example--Coordinate Geometry--Slope Formula: Example 4 Math Example--Coordinate Geometry--Slope Formula: Example 4

Topic

Slope Formula

Description

This example illustrates the calculation of slope for a vertical line passing through points (5, 8) and (5, 2) on a coordinate grid. When we apply the slope formula, we find that the slope is (8 - 2) / (5 - 5) = 6 / 0, which is undefined.

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 vertical, resulting in an undefined slope.

Slope
Math Example--Coordinate Geometry--Slope Formula: Example 5 Math Example--Coordinate Geometry--Slope Formula: Example 5 Math Example--Coordinate Geometry--Slope Formula: Example 5

Topic

Slope Formula

Description

This example demonstrates the calculation of slope for a line connecting two points in different quadrants: (-6, -2) in Quadrant III and (6, 5) in Quadrant I. Applying the slope formula, we find that the slope is (5 - (-2)) / (6 - (-6)) = 7 / 12 = 1 / 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 5 Math Example--Coordinate Geometry--Slope Formula: Example 5 Math Example--Coordinate Geometry--Slope Formula: Example 5

Topic

Slope Formula

Description

This example demonstrates the calculation of slope for a line connecting two points in different quadrants: (-6, -2) in Quadrant III and (6, 5) in Quadrant I. Applying the slope formula, we find that the slope is (5 - (-2)) / (6 - (-6)) = 7 / 12 = 1 / 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 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 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--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 1 Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 1 Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 1

Topic

Linear Functions

Description

This example demonstrates how to graph a linear function with a slope of 2 and a y-intercept of 3. The process involves three key steps: first, plotting the y-intercept at (0, 3); second, using the slope to find another point on the line; and finally, connecting these points to form the line.

Slope-Intercept Form
Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 10 Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 10 Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 10

Topic

Linear Functions

Description

This example illustrates the process of graphing a linear function with a slope of -4 and a y-intercept of 0. The method involves three main steps: plotting the y-intercept at the origin (0, 0), using the slope to determine a second point on the line, and connecting these points to create the linear graph.

Slope-Intercept Form
Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 11 Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 11 Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 11

Topic

Linear Functions

Description

This example demonstrates the process of graphing a linear function with a slope of 0 and a y-intercept of 5. The procedure involves three key steps: plotting the y-intercept at (0, 5), recognizing that a slope of 0 results in a horizontal line, and drawing the line parallel to the x-axis through the y-intercept.

Slope-Intercept Form
Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 12 Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 12 Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 12

Topic

Linear Functions

Description

This example illustrates the process of graphing a linear function with a slope of 0 and a y-intercept of -5. The method involves three main steps: plotting the y-intercept at (0, -5), recognizing that a slope of 0 results in a horizontal line, and drawing the line parallel to the x-axis through the y-intercept.

Slope-Intercept Form
Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 13 Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 13 Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 13

Topic

Linear Functions

Description

This example demonstrates how to graph a linear function with a slope of 0 and a y-intercept of 0. The process involves recognizing that this special case results in a horizontal line coinciding with the x-axis. The line passes through the origin (0, 0) and extends infinitely in both directions along the x-axis.

Slope-Intercept Form
Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 2 Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 2 Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 2

Topic

Linear Functions

Description

This example illustrates the process of graphing a linear function with a slope of 0.5 and a y-intercept of 3. The method involves three main steps: plotting the y-intercept at (0, 3), using the slope to determine a second point on the line, and connecting these points to create the linear graph.

Slope-Intercept Form
Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 3 Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 3 Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 3

Topic

Linear Functions

Description

This example demonstrates the process of graphing a linear function with a slope of 5 and a y-intercept of -4. The procedure involves three key steps: plotting the y-intercept at (0, -4), using the slope to determine a second point on the line, and connecting these points to form the linear graph.

Slope-Intercept Form
Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 4 Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 4 Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 4

Topic

Linear Functions

Description

This example illustrates the process of graphing a linear function with a slope of 0.1 and a y-intercept of -4. The method involves three main steps: plotting the y-intercept at (0, -4), using the slope to determine a second point on the line, and connecting these points to create the linear graph.

Slope-Intercept Form
Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 5 Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 5 Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 5

Topic

Linear Functions

Description

This example demonstrates how to graph a linear function with a slope of -4 and a y-intercept of 5. The process involves three key steps: first, plotting the y-intercept at (0, 5); second, using the slope to find another point on the line; and finally, connecting these points to form the line.

Slope-Intercept Form
Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 6 Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 6 Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 6

Topic

Linear Functions

Description

This example illustrates the process of graphing a linear function with a slope of -1/3 and a y-intercept of 5. The method involves three main steps: plotting the y-intercept at (0, 5), using the slope to determine a second point on the line, and connecting these points to create the linear graph.

Slope-Intercept Form
Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 7 Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 7 Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 7

Topic

Linear Functions

Description

This example demonstrates the process of graphing a linear function with a slope of -3 and a y-intercept of -2. The procedure involves three key steps: plotting the y-intercept at (0, -2), using the slope to determine a second point on the line, and connecting these points to form the linear graph.

Slope-Intercept Form