Illustrative Math-Media4Math Alignment

 

 

Illustrative Math Alignment: Grade 8 Unit 3

Linear Relationships

Lesson 12: Solutions to Linear Equations

Use the following Media4Math resources with this Illustrative Math lesson.

Thumbnail Image Title Body Curriculum Topic
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 22 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 22 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 22

Topic

Linear Functions

Description

The image shows a graph with two points (5, 1) and (8, -5) marked on a coordinate plane. The example demonstrates how to find the equation of a line using these two points. The slope is calculated using the slope formula, and then the point-slope form is applied to derive the equation of the line. The slope is calculated as (1 - (-5)) / (5 - 8) = -2. Using point-slope form: y - 1 = -2(x - 5), which simplifies to y = -2x + 11.

 Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 23 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 23 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 23

Topic

Linear Functions

Description

The image shows a graph with two points (6, 1) and (6, -5) marked on a coordinate plane. The example demonstrates how to find the equation of a vertical line using these two points. Since both x-coordinates are equal, the slope is undefined, indicating a vertical line. The slope is undefined because x-values are equal: (1 - (-5)) / (6 - 6) = undefined. This means it's a vertical line at x = 6.

 Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 24 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 24 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 24

Topic

Linear Functions

Description

The image shows a graph with two points (-6, -2) and (-3, 4) marked on a coordinate plane. The example demonstrates how to find the equation of a line using these two points. The slope is calculated using the slope formula, and then the point-slope form is applied to derive the equation of the line. The slope is calculated as (4 - (-2)) / (-3 - (-6)) = 2. Using point-slope form: y - 4 = 2(x + 3), which simplifies to y = 2x + 10.

 Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 25 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 25 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 25

Topic

Linear Functions

Description

A graph with two points (-8, 6) and (-3, -4) marked on a coordinate plane. The slope is calculated using the formula (y2 - y1) / (x2 - x1), and the equation of the line is derived using the point-slope form. The final equation is y = -2x - 10. The slope is calculated as (-4 - 6) / (-3 - (-8)) = -2. Using the point-slope form y - y1 = m(x - x1), the equation becomes y - 6 = -2(x + 8), which simplifies to y = -2x - 10.

 Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 26 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 26 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 26

Topic

Linear Functions

Description

A graph with two points (-8, -6) and (4, 2) marked on a coordinate plane. The slope is calculated using the formula (y2 - y1) / (x2 - x1), and the equation of the line is derived using the point-slope form. The final equation is y = 1/4 x - 3. The slope is calculated as (2 + 6) / (4 + 8) = 1/4. Using the point-slope form y - y1 = m(x - x1), the equation becomes y + 2 = 1/4(x - 4), which simplifies to y = 1/4 x - 3.

 Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 27 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 27 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 27

Topic

Linear Functions

Description

A graph with two points (-3, 4) and (-3, -5) marked on a coordinate plane. The slope is undefined because both x-coordinates are equal, leading to division by zero. This represents a vertical line at x = -3. The slope is undefined because (4 + 5) / (-3 + 3) results in division by zero. This indicates a vertical line at x = -3.

 Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 28 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 28 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 28

Topic

Linear Functions

Description

A graph with two points (-6, -1) and (6, 4) marked on a coordinate plane. The slope is calculated using the formula (y2 - y1) / (x2 - x1), and the equation of the line is derived using the point-slope form. The final equation is y = -(1/4)x - 2.5 or -(1/4)x - (5/2). The slope is calculated as (4 + 1) / (6 + 6) = -(1/4). Using the point-slope form y - y1 = m(x - x1), the equation becomes y + 1 = -(1/4)(x + 6), which simplifies to y = -(1/4)x - (5/2).

 Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 29 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 29 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 29

Topic

Linear Functions

 Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 3 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 3 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 3

Topic

Linear Functions

Description

This example demonstrates how to find the equation of a horizontal line passing through the points (2, 3) and (7, 3). The slope is calculated as 0 since both y-coordinates are the same. Using the point-slope form, y - y1 = m(x - x1), the equation becomes y - 3 = 0(x - any x-value), which simplifies to y = 3, representing a horizontal line.

 Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 4 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 4 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 4

Topic

Linear Functions

Description

This example illustrates how to find the equation of a vertical line passing through the points (5, 3) and (5, 8). The slope is undefined because both x-coordinates are the same, resulting in division by zero when using the slope formula. This indicates a vertical line, and the equation 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 5 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 5 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 5

Topic

Linear Functions

Description

This example demonstrates how to find the equation of a line passing through the points (-6, 1) and (-2, 3). The slope is calculated using the formula (y2 - y1) / (x2 - x1), resulting in a slope of 1/2. Using the point-slope form of a line, y - y1 = m(x - x1), the equation is derived and simplified to y = (1/2)x + 4.

 Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 6 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 6 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 6

Topic

Linear Functions

Description

This image shows a graph with two points (-8, 4) and (-4, 2). The slope is calculated as (y2 - y1) / (x2 - x1), resulting in a slope of -1/2. The equation of the line is derived using point-slope form and simplified to y = -(1/2)x. The slope is calculated as -1/2, and the line equation is determined using point-slope form: y = -(1/2)x.

 Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 7 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 7 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 7

Topic

Linear Functions

Description

This image shows a graph with two points (-7, 5) and (-1, 5). The slope is calculated as zero since the y-values are equal. The equation of the line is horizontal, simplified to y = 5. The slope is 0, indicating a horizontal line. The equation is y = 5.

 Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 8 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 8 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 8

Topic

Linear Functions

Description

This image shows a graph with two points (-5, 6) and (-5, 3). The slope is undefined because the x-values are equal. This results in a vertical line at x = -5. The slope is undefined, indicating a vertical line at x = -5.

 Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 9 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 9 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 9

Topic

Linear Functions

Description

The image shows a coordinate plane with two points (-5, -4) and (-4, -1) 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) = (-1 - (-4)) / (-4 - (-5)) = 3 / 1 = 3. Using point-slope form, y - y1 = m(x - x1), the equation is derived as y + 1 = 3(x + 4), which simplifies to y = 3x + 11.

 Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Point-Slope Formula: Example 1 Math Example--Linear Function Concepts--The Point-Slope Formula: Example 1 Math Example--Linear Function Concepts--The Point-Slope Formula: Example 1

Topic

The Point-Slope Form

Description

This example demonstrates how to find the equation of a line using the point-slope form. The given information includes a slope of 5 and a point (6, 5) through which the line passes. Using the point-slope formula y - y1 = m(x - x1), we can substitute the known values to derive the equation y - 5 = 5(x - 6). Simplifying this equation leads to the final result: y = 5x - 25.

 Point-Slope Form
Math Example--Linear Function Concepts--The Point-Slope Formula: Example 2 Math Example--Linear Function Concepts--The Point-Slope Formula: Example 2 Math Example--Linear Function Concepts--The Point-Slope Formula: Example 2

Topic

The Point-Slope Form

Description

In this example, we explore finding the equation of a line with a slope of -1 passing through the point (5, 2). Applying the point-slope formula y - y1 = m(x - x1), we substitute the given values to obtain y - 2 = -(x - 5). After simplification, the final equation of the line is y = -x + 7.

 Point-Slope Form
Math Example--Linear Function Concepts--The Point-Slope Formula: Example 3 Math Example--Linear Function Concepts--The Point-Slope Formula: Example 3 Math Example--Linear Function Concepts--The Point-Slope Formula: Example 3

Topic

The Point-Slope Form

Description

This example demonstrates the application of the point-slope formula to find the equation of a line with a slope of 3 passing through the point (-2, 7). Using the formula y - y1 = m(x - x1), we substitute the given values to get y - 7 = 3(x - (-2)). After simplification, the resulting equation is y = 3x + 13.

 Point-Slope Form
Math Example--Linear Function Concepts--The Point-Slope Formula: Example 4 Math Example--Linear Function Concepts--The Point-Slope Formula: Example 4 Math Example--Linear Function Concepts--The Point-Slope Formula: Example 4

Topic

The Point-Slope Form

Description

In this example, we explore finding the equation of a line with a slope of -5 that passes through the point (-7, 5). Applying the point-slope formula y - y1 = m(x - x1), we substitute the given values to obtain y - 5 = -5(x - (-7)). After simplification, the final equation of the line is y = -5x - 30.

 Point-Slope Form
Math Example--Linear Function Concepts--The Point-Slope Formula: Example 5 Math Example--Linear Function Concepts--The Point-Slope Formula: Example 5 Math Example--Linear Function Concepts--The Point-Slope Formula: Example 5

Topic

The Point-Slope Form

Description

This example demonstrates the application of the point-slope formula to find the equation of a line with a slope of 2 passing through the point (-2, -3). Using the formula y - y1 = m(x - x1), we substitute the given values to get y - (-3) = 2(x - (-2)). After simplification, the resulting equation is y = 2x + 1.

 Point-Slope Form
Math Example--Linear Function Concepts--The Point-Slope Formula: Example 6 Math Example--Linear Function Concepts--The Point-Slope Formula: Example 6 Math Example--Linear Function Concepts--The Point-Slope Formula: Example 6

Topic

The Point-Slope Form

Description

This example demonstrates the application of the point-slope formula to find the equation of a line with a slope of -7 passing through the point (-8, -5). Using the formula y - y1 = m(x - x1), we substitute the given values to get y - (-5) = -7(x - (-8)). After simplification, the resulting equation is y = -7x - 61.

 Point-Slope Form
Math Example--Linear Function Concepts--The Point-Slope Formula: Example 7 Math Example--Linear Function Concepts--The Point-Slope Formula: Example 7 Math Example--Linear Function Concepts--The Point-Slope Formula: Example 7

Topic

The Point-Slope Form

Description

In this example, we explore finding the equation of a line with a slope of 4 passing through the point (8, -2). Applying the point-slope formula y - y1 = m(x - x1), we substitute the given values to obtain y - (-2) = 4(x - 8). After simplification, the final equation of the line is y = 4x - 34.

 Point-Slope Form
Math Example--Linear Function Concepts--The Point-Slope Formula: Example 8 Math Example--Linear Function Concepts--The Point-Slope Formula: Example 8 Math Example--Linear Function Concepts--The Point-Slope Formula: Example 8

Topic

The Point-Slope Form

Description

This example demonstrates the application of the point-slope formula to find the equation of a line with a slope of -2 passing through the point (3, -8). Using the formula y - y1 = m(x - x1), we substitute the given values to get y - (-8) = -2(x - 3). After simplification, the resulting equation is y = -2x - 2.

 Point-Slope Form
Math Examples Math Example: The Slope As Rise Over Run: Three Examples

In this set of math examples, see how slope is calculated for a staircase based on measures for the rise and the run.

 Slope
MATH EXAMPLES--Teacher's Guide: Finding the Equation of a Line, Given Two Points MATH EXAMPLES--Teacher's Guide: Finding the Equation of a Line, Given Two Points MATH EXAMPLES--Teacher's Guide: Finding the Equation of a Line, Given Two Points

This Teacher's Guide provides an overview of the 12 worked-out examples that show how to find the equation of a line, given two points.

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 Applications of Linear Functions and Graphs of Linear Functions
MATH EXAMPLES--Teacher's Guide: The Midpoint Formula MATH EXAMPLES--Teacher's Guide: The Midpoint Formula MATH EXAMPLES--Teacher's Guide: The Midpoint Formula

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MATH EXAMPLES--Teacher's Guide: The Slope Formula MATH EXAMPLES--Teacher's Guide: The Slope Formula MATH EXAMPLES--Teacher's Guide: The Slope Formula

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 Applications of Linear Functions and Slope
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Paper-and-Pencil Quiz: Equation of a Line Given Two Points (Easy) Paper-and-Pencil Quiz: Equation of a Line Given Two Points (Easy) Paper-and-Pencil Quiz: Equation of a Line Given Two Points (Easy)

This is part of a collection of math quizzes on the topic of finding the Equation of a Line Given Two Points.

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 Slope
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 Slope
Paper-and-Pencil Quiz: Slope Formula (Medium) Paper-and-Pencil Quiz: Slope Formula (Medium) Paper-and-Pencil Quiz: Slope Formula (Medium)

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 Slope
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Honey bees not only produce a tasty treat, they also help pollinate flowering plants that provide much of the food throughout the world. So, when in 2006 bee colonies started dying out, scientists recognized a serious problem. Analyzing statistics from honey bee production allows for a mathematical analysis of the so-called Colony Collapse Disorder. Note: The download for this resources is the Promethean Flipchart.

To access the full video [Algebra Applications: Variables and Equations, Segment 2: Honey Production]:  https://www.media4math.com/library/algebra-applications-variables-and-equations-segment-2-honey-production

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Find the slope of the line connecting two points in this 20-flash card set. The integers are in the range -20 to 20.

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To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/36XwrY6 		Slope