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Illustrative Math-Media4Math Alignment

 

 

Illustrative Math Alignment: Grade 7 Unit 7

Expressions, Equations, and Inequalities

Lesson 8: Reasoning about Solving Equations (Part 2)

Use the following Media4Math resources with this Illustrative Math lesson.

Thumbnail Image Title Body Curriculum Topic
Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 20 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 20 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 20

Topic

Linear Functions

Description

This example demonstrates the conversion of the linear equation -14x - 35y = 0 from standard form to slope-intercept form. The process involves isolating y and dividing by its coefficient, resulting in y = -2/5 x. This transformation clearly reveals the slope and y-intercept of the line.

Standard Form
Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 21 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 21 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 21

Topic

Linear Functions

Description

This example showcases the transformation of the linear equation 28x - 21y = 0 from standard form to slope-intercept form. The process involves isolating y and dividing by its coefficient, resulting in y = 4/3 x. This step-by-step solution clearly reveals the slope and y-intercept of the line.

Standard Form
Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 22 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 22 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 22

Topic

Linear Functions

Description

This example illustrates the conversion of the linear equation -13x + 39y = 0 from standard form to slope-intercept form. The solution involves isolating y and dividing by its coefficient, resulting in y = 1/3 x. This process clearly reveals the slope and y-intercept of the line.

Standard Form
Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 3 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 3 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 3

Topic

Linear Functions

Description

This example showcases the transformation of the linear equation 5x - 2y = 12 from standard form to slope-intercept form. The process involves isolating y and dividing by its coefficient, resulting in y = 2.5x - 6. This step-by-step solution clearly reveals the slope and y-intercept of the line.

Standard Form
Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 4 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 4 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 4

Topic

Linear Functions

Description

This example demonstrates the conversion of the linear equation -6x + 10y = 20 from standard form to slope-intercept form. The solution process involves isolating y and dividing by its coefficient, resulting in y = 0.6x + 2. This transformation clearly reveals the slope and y-intercept of the line.

Standard Form
Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 5 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 5 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 5

Topic

Linear Functions

Description

This example illustrates the process of converting the linear equation -9x - 15y = -45 from standard form to slope-intercept form. The solution involves rearranging the equation to isolate y, resulting in y = 3/5 x + 3. This transformation clearly reveals the slope and y-intercept of the line.

Standard Form
Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 6 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 6 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 6

Topic

Linear Functions

Description

This example demonstrates the conversion of the linear equation -8x - 12y = 25 from standard form to slope-intercept form. The process involves manipulating the equation to solve for y, yielding y = -2/3 x - 25/12. This transformation clearly reveals the slope and y-intercept of the line.

Standard Form
Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 7 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 7 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 7

Topic

Linear Functions

Description

This example illustrates the transformation of the linear equation -2x + 16y = -36 from standard form to slope-intercept form. The solution process involves solving for y, resulting in y = 1/8 x - 9/4. This step-by-step conversion clearly reveals the slope and y-intercept of the line.

Standard Form
Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 8 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 8 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 8

Topic

Linear Functions

Description

This example showcases the conversion of the linear equation -7x + 21y = 63 from standard form to slope-intercept form. The process involves rearranging the equation to isolate y, resulting in y = 1/3 x + 3. This transformation clearly reveals the slope and y-intercept of the line.

Standard Form
Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 9 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 9 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 9

Topic

Linear Functions

Description

This example demonstrates the process of converting the linear equation 10x - 28y = 56 from standard form to slope-intercept form. The solution involves isolating y and dividing by its coefficient, resulting in y = (5/14)x - 2. This transformation clearly reveals the slope and y-intercept of the line.

Standard 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 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 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 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 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 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 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 21 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 21 Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 21

Topic

Linear Functions

Description

The image shows a graph with two points (2, -4) and (6, 1) 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 - (-4)) / (6 - 2) = 5 / 4. Using point-slope form: y - 1 = (5 / 4)(x - 6), which simplifies to y = 5/4x - 6 1/2.

Point-Slope Form and Slope-Intercept Form
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--Percents-- Equations with Percents: Example 1 Math Example--Percents--Equations with Percents: Example 1 Math Example--Percents--Equations with Percents: Example 1

Topic

Solving Equations

Description

This math example focuses on solving percent equations, specifically asking "What is 5% of 8?" The solution involves converting 5% to its decimal form, 0.05, and then multiplying it by 8 to get the result of 0.4. This straightforward approach demonstrates how to tackle basic percent calculations efficiently.

Solving Percent Equations
Math Example--Percents-- Equations with Percents: Example 10 Math Example--Percents--Equations with Percents: Example 10 Math Example--Percents--Equations with Percents: Example 10

Topic

Solving Equations

Description

This math example demonstrates solving percent equations by asking "What is 170% of 9.5?" The solution involves converting 170% to its decimal equivalent, 1.7, and then multiplying it by 9.5 to obtain the result of 16.15. This example combines a percentage greater than 100% with a decimal base number, further illustrating the versatility of the percent-to-decimal conversion method in complex scenarios.

Solving Percent Equations
Math Example--Percents-- Equations with Percents: Example 11 Math Example--Percents--Equations with Percents: Example 11 Math Example--Percents--Equations with Percents: Example 11

Topic

Solving Equations

Description

This math example focuses on solving percent equations, specifically asking "What is 225.5% of 78?" The solution involves converting 225.5% to its decimal form, 2.255, and then multiplying it by 78 to arrive at the answer of 175.89. This example introduces a decimal percentage greater than 200% and a larger whole number as the base value, demonstrating the scalability and flexibility of the percent-to-decimal conversion method in complex scenarios.

Solving Percent Equations
Math Example--Percents-- Equations with Percents: Example 12 Math Example--Percents--Equations with Percents: Example 12 Math Example--Percents--Equations with Percents: Example 12

Topic

Solving Equations

Description

This math example demonstrates solving percent equations by asking "What is 400% of 92.8?" The solution involves converting 400% to its decimal equivalent, 4.0, and then multiplying it by 92.8 to obtain the result of 371.2. This example showcases how to handle percentages greater than 100% and their application to decimal numbers, illustrating the versatility of the percent-to-decimal conversion method in complex scenarios.

Solving Percent Equations
Math Example--Percents-- Equations with Percents: Example 13 Math Example--Percents--Equations with Percents: Example 13 Math Example--Percents--Equations with Percents: Example 13

Topic

Solving Equations

Description

This math example focuses on solving percent equations by asking "5 is what percent of 9?" The solution involves setting up the equation 9 * (x / 100) = 5, then solving for x to get x = 5 * (100 / 9), which is approximately 55.56%. This example introduces a new type of percent problem where students must find the percentage given two known values.

Solving Percent Equations
Math Example--Percents-- Equations with Percents: Example 14 Math Example--Percents--Equations with Percents: Example 14 Math Example--Percents--Equations with Percents: Example 14

Topic

Solving Equations

Description

This math example demonstrates solving percent equations by asking "6 is what percent of 2.3?" The solution involves setting up the equation 2.3 * (x / 100) = 6, then solving for x to get x = 6 * (100 / 2.3), which is approximately 260.87%. This example introduces a scenario where the resulting percentage is greater than 100% and involves a decimal base number.

Solving Percent Equations
Math Example--Percents-- Equations with Percents: Example 15 Math Example--Percents--Equations with Percents: Example 15 Math Example--Percents--Equations with Percents: Example 15

Topic

Solving Equations

Description

This math example focuses on solving percent equations by asking "9 is what percent of 38?" The solution involves setting up the equation 38 * (x / 100) = 9, then solving for x to get x = 9 * (100 / 38), which is approximately 23.68%. This example demonstrates how to calculate a percentage when the first number is smaller than the second, resulting in a percentage less than 100%.

Solving Percent Equations
Math Example--Percents-- Equations with Percents: Example 16 Math Example--Percents--Equations with Percents: Example 16 Math Example--Percents--Equations with Percents: Example 16

Topic

Solving Equations

Description

This math example demonstrates solving percent equations by asking "2 is what percent of 55.5?" The solution involves setting up the equation 55.5 * (x / 100) = 2, then solving for x to get x = 2 * (100 / 55.5), which is approximately 3.6036%. This example introduces a scenario where the resulting percentage is a small fraction, less than 5%, and involves a decimal base number.

Solving Percent Equations
Math Example--Percents-- Equations with Percents: Example 17 Math Example--Percents--Equations with Percents: Example 17 Math Example--Percents--Equations with Percents: Example 17

Topic

Solving Equations

Description

This math example focuses on solving percent equations by asking "8 is what percent of 120?" The solution involves setting up the equation 120 * (x / 100) = 8, then solving for x to get x = 8 * (100 / 120), which is approximately 6.67%. This example demonstrates how to calculate a percentage when dealing with larger whole numbers, resulting in a percentage less than 10%.

Solving Percent Equations
Math Example--Percents-- Equations with Percents: Example 18 Math Example--Percents--Equations with Percents: Example 18 Math Example--Percents--Equations with Percents: Example 18

Topic

Solving Equations

Description

This math example demonstrates solving percent equations by asking "3.5 is what percent of 350?" The solution involves setting up the equation 350 * (x / 100) = 3.5, then solving for x to get x = 3.5 * (100 / 350), which equals 1%. This example introduces a scenario where the resulting percentage is a whole number (1%) and involves a decimal number as the first value.

Solving Percent Equations
Math Example--Percents-- Equations with Percents: Example 19 Math Example--Percents--Equations with Percents: Example 19 Math Example--Percents--Equations with Percents: Example 19

Topic

Solving Equations

Description

This math example focuses on solving percent equations by asking "12 is what percent of 8?" The solution involves setting up the equation 8 * (x / 100) = 12, then solving for x to get x = 12 * (100 / 8), which equals 150%. This example demonstrates how to calculate a percentage when the first number is larger than the second, resulting in a percentage greater than 100%.

Solving Percent Equations