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Illustrative Math-Media4Math Alignment

 

 

Illustrative Math Alignment: Grade 7 Unit 7

Expressions, Equations, and Inequalities

Lesson 10: Different Options for Solving One Equation

Use the following Media4Math resources with this Illustrative Math lesson.

Thumbnail Image Title Body Curriculum Topic
Math Clip Art--The Language of Math--Numbers and Equations, Image 47 Math Clip Art--The Language of Math--Numbers and Equations 47 Math Clip Art--The Language of Math--Numbers and Equations 47

Topic

The Language of Math

Description

This image presents the equation "2/2=1" in both numerical and word form. It continues the progression of division concepts, now working with a fraction where the numerator and denominator are equal.

The dual representation of the equation reinforces the connection between mathematical symbols and their verbal expressions. This visual aid is crucial in developing number sense and understanding the concept of division, particularly how dividing a number by itself always results in 1.

 Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations, Image 48 Math Clip Art--The Language of Math--Numbers and Equations 48 Math Clip Art--The Language of Math--Numbers and Equations 48

Topic

The Language of Math

Description

This clip art from the Language of Math collection illustrates the equation "3/3=1" in both numerical and word form. It continues the series of division concepts, focusing on fractions where the numerator and denominator are equal.

The simultaneous presentation of the equation in symbols and words strengthens the connection between mathematical language and everyday language. This visual representation helps students understand how division works and reinforces the concept that any number divided by itself equals 1.

 Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations, Image 49 Math Clip Art--The Language of Math--Numbers and Equations 49 Math Clip Art--The Language of Math--Numbers and Equations 49

Topic

The Language of Math

Description

This image presents the equation "4/2=2" in both numerical and word form. It advances the complexity of division concepts by introducing a fraction where the numerator is greater than the denominator.

The dual representation of the equation reinforces the connection between mathematical symbols and their verbal expressions. This visual aid is crucial in developing number sense and understanding the concept of division, particularly how dividing by a smaller number results in a larger quotient.

 Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations, Image 50 Math Clip Art--The Language of Math--Numbers and Equations 50 Math Clip Art--The Language of Math--Numbers and Equations 50

Topic

The Language of Math

Description

This clip art from the Language of Math collection illustrates the equation "5/1=5" in both numerical and word form. It introduces the concept of dividing by 1, which is a fundamental principle in mathematics.

The simultaneous presentation of the equation in symbols and words strengthens the connection between mathematical language and everyday language. This visual representation helps students understand that dividing a number by 1 results in the same number, reinforcing the identity property of division.

 Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations, Image 51 Math Clip Art--The Language of Math--Numbers and Equations 51 Math Clip Art--The Language of Math--Numbers and Equations 51

Topic

The Language of Math

Description

This image presents the equation "6/2=3" in both numerical and word form. It continues the progression of division concepts, now working with larger numbers and introducing the concept of halving.

The dual representation of the equation reinforces the connection between mathematical symbols and their verbal expressions. This visual aid is crucial in developing number sense and understanding the concept of division, particularly how dividing by 2 relates to finding half of a number.

 Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations, Image 52 Math Clip Art--The Language of Math--Numbers and Equations 52 Math Clip Art--The Language of Math--Numbers and Equations 52

Topic

The Language of Math

Description

This clip art from the Language of Math collection illustrates the equation "7/7=1" in both numerical and word form. It reinforces the concept that any number divided by itself equals 1.

The simultaneous presentation of the equation in symbols and words strengthens the connection between mathematical language and everyday language. This visual representation helps students understand a fundamental principle of division and introduces the concept of equivalent fractions.

 Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations, Image 53 Math Clip Art--The Language of Math--Numbers and Equations 53 Math Clip Art--The Language of Math--Numbers and Equations 53

Topic

The Language of Math

Description

This image presents the equation "8/4=2" in both numerical and word form. It advances the complexity of division concepts by introducing division with larger numbers and the concept of quartering.

The dual representation of the equation reinforces the connection between mathematical symbols and their verbal expressions. This visual aid is crucial in developing number sense and understanding the concept of division, particularly how dividing by 4 relates to finding a quarter of a number.

 Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations, Image 54 Math Clip Art--The Language of Math--Numbers and Equations 54 Math Clip Art--The Language of Math--Numbers and Equations 54

Topic

The Language of Math

Description

This clip art from the Language of Math collection illustrates the equation "9/3=3" in both numerical and word form. It continues the progression of division concepts, now working with larger numbers and introducing the concept of thirds.

The simultaneous presentation of the equation in symbols and words strengthens the connection between mathematical language and everyday language. This visual representation helps students understand how division works with larger numbers and reinforces the concept of equal sharing.

 Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations, Image 55 Math Clip Art--The Language of Math--Numbers and Equations 55 Math Clip Art--The Language of Math--Numbers and Equations 55

Topic

The Language of Math

Description

This image presents the equation "10/2=5" in both numerical and word form. It continues the progression of division concepts, now working with larger numbers and reinforcing the concept of halving.

The dual representation of the equation reinforces the connection between mathematical symbols and their verbal expressions. This visual aid is crucial in developing number sense and understanding the concept of division, particularly how dividing by 2 relates to finding half of a number, even with larger values.

 Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations, Image 56 Math Clip Art--The Language of Math--Numbers and Equations 56 Math Clip Art--The Language of Math--Numbers and Equations 56

Topic

The Language of Math

Description

This clip art from the Language of Math collection illustrates the equation "11/1=11" in both numerical and word form. It introduces the concept of dividing by 1, which is a fundamental principle in mathematics.

The simultaneous presentation of the equation in symbols and words strengthens the connection between mathematical language and everyday language. This visual representation helps students understand that dividing a number by 1 results in the same number, reinforcing the identity property of division.

 Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations, Image 57 Math Clip Art--The Language of Math--Numbers and Equations 57 Math Clip Art--The Language of Math--Numbers and Equations 57

Topic

The Language of Math

Description

This image presents the equation "12/3=4" in both numerical and word form. It advances the complexity of division concepts by working with larger numbers and introducing the concept of dividing by 3.

The dual representation of the equation reinforces the connection between mathematical symbols and their verbal expressions. This visual aid is crucial in developing number sense and understanding the concept of division, particularly how dividing by 3 relates to grouping numbers into thirds.

 Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations, Image 58 Math Clip Art--The Language of Math--Numbers and Equations 58 Math Clip Art--The Language of Math--Numbers and Equations 58

Topic

The Language of Math

Description

This clip art from the Language of Math collection illustrates the equation "13/13=1" in both numerical and word form. It reinforces the concept that any number divided by itself equals 1, now using a larger number.

The simultaneous presentation of the equation in symbols and words strengthens the connection between mathematical language and everyday language. This visual representation helps students understand a fundamental principle of division and introduces the concept of equivalent fractions with larger numbers.

 Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations, Image 59 Math Clip Art--The Language of Math--Numbers and Equations 59 Math Clip Art--The Language of Math--Numbers and Equations 59

Topic

The Language of Math

Description

This image presents the equation "14/7=2" in both numerical and word form. It continues the progression of division concepts, now working with larger numbers and introducing the concept of halving with two-digit numbers.

The dual representation of the equation reinforces the connection between mathematical symbols and their verbal expressions. This visual aid is crucial in developing number sense and understanding the concept of division, particularly how dividing by half of a number results in 2.

 Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations, Image 60 Math Clip Art--The Language of Math--Numbers and Equations 60 Math Clip Art--The Language of Math--Numbers and Equations 60

Topic

The Language of Math

Description

This clip art from the Language of Math collection illustrates the equation "15/3=5" in both numerical and word form. It advances the complexity of division concepts by working with larger numbers and introducing the concept of dividing by 3.

The simultaneous presentation of the equation in symbols and words strengthens the connection between mathematical language and everyday language. This visual representation helps students understand how division works with larger numbers and reinforces the concept of grouping into thirds.

 Numerical Expressions
Math Clip Art--The Language of Math--Numbers and Equations, Image 61 Math Clip Art--The Language of Math--Numbers and Equations 61 Math Clip Art--The Language of Math--Numbers and Equations 61

Topic

The Language of Math

Description

This image presents a blank card, serving as the final piece in the series of 61 clip art images focused on the Language of Math: Numbers and Equations. While it doesn't contain a specific equation, its presence is significant in the collection.

 Numerical Expressions
Math Clip Art Math Clip Art: Equations vs. Inequalities Math Clip Art: Equations vs. Inequalities

This collection of clip art images show the contrast between graphs of equations and inequalities for one- and two-variable graphs.

 Inequalities
Math Clip Art: Solving Equations and Inequalities Math Clip Art: Solving Equations and Inequalities Math Clip Art: Solving Equations and Inequalities

Use these clip art images to show how to solve linear equations and inequalities. Examples include situations where the inequality symbol changes.

 Inequalities
Math Example--Function Concepts--Function Rules and Equations--Example 1 Math Example--Function Concepts--Function Rules and Equations--Example 1 Math Example--Function Concepts--Function Rules and Equations--Example 1

This is part of a collection of math examples that focus on function concepts.

 Relations and Functions
Math Example--Function Concepts--Function Rules and Equations--Example 10 Math Example--Function Concepts--Function Rules and Equations--Example 10 Math Example--Function Concepts--Function Rules and Equations--Example 10

This is part of a collection of math examples that focus on function concepts.

 Relations and Functions
Math Example--Function Concepts--Function Rules and Equations--Example 2 Math Example--Function Concepts--Function Rules and Equations--Example 2 Math Example--Function Concepts--Function Rules and Equations--Example 2

This is part of a collection of math examples that focus on function concepts.

 Relations and Functions
Math Example--Function Concepts--Function Rules and Equations--Example 3 Math Example--Function Concepts--Function Rules and Equations--Example 3 Math Example--Function Concepts--Function Rules and Equations--Example 3

This is part of a collection of math examples that focus on function concepts.

 Relations and Functions
Math Example--Function Concepts--Function Rules and Equations--Example 4 Math Example--Function Concepts--Function Rules and Equations--Example 4 Math Example--Function Concepts--Function Rules and Equations--Example 4

This is part of a collection of math examples that focus on function concepts.

 Relations and Functions
Math Example--Function Concepts--Function Rules and Equations--Example 5 Math Example--Function Concepts--Function Rules and Equations--Example 5 Math Example--Function Concepts--Function Rules and Equations--Example 5

This is part of a collection of math examples that focus on function concepts.

 Relations and Functions
Math Example--Function Concepts--Function Rules and Equations--Example 6 Math Example--Function Concepts--Function Rules and Equations--Example 6 Math Example--Function Concepts--Function Rules and Equations--Example 6

This is part of a collection of math examples that focus on function concepts.

 Relations and Functions
Math Example--Function Concepts--Function Rules and Equations--Example 7 Math Example--Function Concepts--Function Rules and Equations--Example 7 Math Example--Function Concepts--Function Rules and Equations--Example 7

This is part of a collection of math examples that focus on function concepts.

 Relations and Functions
Math Example--Function Concepts--Function Rules and Equations--Example 8 Math Example--Function Concepts--Function Rules and Equations--Example 8 Math Example--Function Concepts--Function Rules and Equations--Example 8

This is part of a collection of math examples that focus on function concepts.

 Relations and Functions
Math Example--Function Concepts--Function Rules and Equations--Example 9 Math Example--Function Concepts--Function Rules and Equations--Example 9 Math Example--Function Concepts--Function Rules and Equations--Example 9

This is part of a collection of math examples that focus on function concepts.

 Relations and Functions
Math Example--Graphical Solutions to Rational Equations--Example 1 Math Example--Graphical Solutions to Rational Equations--Example 1 This is part of a collection of math examples that show how to use graphical techniques to solve rational equations. Note: The download is an image file.

Related Resources

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Create a Slide Show

Subscribers can use Slide Show Creator to create a slide show from the complete collection of math examples on this topic. To see the complete clip art collection, click on this Link. To learn more about Slide Show Creator, click on this Link: 

Accessibility

This resource can also be used with a screen reader. 		Rational Functions and Equations
Math Example--Graphical Solutions to Rational Equations--Example 10 Math Example--Graphical Solutions to Rational Equations--Example 10 This is part of a collection of math examples that show how to use graphical techniques to solve rational equations. Note: The download is an image file.

Related Resources

To see additional resources on this topic, click on the Related Resources tab.

Create a Slide Show

Subscribers can use Slide Show Creator to create a slide show from the complete collection of math examples on this topic. To see the complete clip art collection, click on this Link. To learn more about Slide Show Creator, click on this Link: 

Accessibility

This resource can also be used with a screen reader. 		Rational Functions and Equations
Math Example--Graphical Solutions to Rational Equations--Example 2 Math Example--Graphical Solutions to Rational Equations--Example 2 This is part of a collection of math examples that show how to use graphical techniques to solve rational equations. Note: The download is an image file.

Related Resources

To see additional resources on this topic, click on the Related Resources tab.

Create a Slide Show

Subscribers can use Slide Show Creator to create a slide show from the complete collection of math examples on this topic. To see the complete clip art collection, click on this Link. To learn more about Slide Show Creator, click on this Link: 

Accessibility

This resource can also be used with a screen reader. 		Rational Functions and Equations
Math Example--Graphical Solutions to Rational Equations--Example 3 Math Example--Graphical Solutions to Rational Equations--Example 3 This is part of a collection of math examples that show how to use graphical techniques to solve rational equations. Note: The download is an image file.

Related Resources

To see additional resources on this topic, click on the Related Resources tab.

Create a Slide Show

Subscribers can use Slide Show Creator to create a slide show from the complete collection of math examples on this topic. To see the complete clip art collection, click on this Link. To learn more about Slide Show Creator, click on this Link: 

Accessibility

This resource can also be used with a screen reader. 		Rational Functions and Equations
Math Example--Graphical Solutions to Rational Equations--Example 4 Math Example--Graphical Solutions to Rational Equations--Example 4 This is part of a collection of math examples that show how to use graphical techniques to solve rational equations. Note: The download is an image file.

Related Resources

To see additional resources on this topic, click on the Related Resources tab.

Create a Slide Show

Subscribers can use Slide Show Creator to create a slide show from the complete collection of math examples on this topic. To see the complete clip art collection, click on this Link. To learn more about Slide Show Creator, click on this Link: 

Accessibility

This resource can also be used with a screen reader. 		Rational Functions and Equations
Math Example--Graphical Solutions to Rational Equations--Example 5 Math Example--Graphical Solutions to Rational Equations--Example 5 This is part of a collection of math examples that show how to use graphical techniques to solve rational equations. Note: The download is an image file.

Related Resources

To see additional resources on this topic, click on the Related Resources tab.

Create a Slide Show

Subscribers can use Slide Show Creator to create a slide show from the complete collection of math examples on this topic. To see the complete clip art collection, click on this Link. To learn more about Slide Show Creator, click on this Link: 

Accessibility

This resource can also be used with a screen reader. 		Rational Functions and Equations
Math Example--Graphical Solutions to Rational Equations--Example 6 Math Example--Graphical Solutions to Rational Equations--Example 6 This is part of a collection of math examples that show how to use graphical techniques to solve rational equations. Note: The download is an image file.

Related Resources

To see additional resources on this topic, click on the Related Resources tab.

Create a Slide Show

Subscribers can use Slide Show Creator to create a slide show from the complete collection of math examples on this topic. To see the complete clip art collection, click on this Link. To learn more about Slide Show Creator, click on this Link: 

Accessibility

This resource can also be used with a screen reader. 		Rational Functions and Equations
Math Example--Graphical Solutions to Rational Equations--Example 7 Math Example--Graphical Solutions to Rational Equations--Example 7 This is part of a collection of math examples that show how to use graphical techniques to solve rational equations. Note: The download is an image file.

Related Resources

To see additional resources on this topic, click on the Related Resources tab.

Create a Slide Show

Subscribers can use Slide Show Creator to create a slide show from the complete collection of math examples on this topic. To see the complete clip art collection, click on this Link. To learn more about Slide Show Creator, click on this Link: 

Accessibility

This resource can also be used with a screen reader. 		Rational Functions and Equations
Math Example--Graphical Solutions to Rational Equations--Example 8 Math Example--Graphical Solutions to Rational Equations--Example 8 This is part of a collection of math examples that show how to use graphical techniques to solve rational equations. Note: The download is an image file.

Related Resources

To see additional resources on this topic, click on the Related Resources tab.

Create a Slide Show

Subscribers can use Slide Show Creator to create a slide show from the complete collection of math examples on this topic. To see the complete clip art collection, click on this Link. To learn more about Slide Show Creator, click on this Link: 

Accessibility

This resource can also be used with a screen reader. 		Rational Functions and Equations
Math Example--Graphical Solutions to Rational Equations--Example 9 Math Example--Graphical Solutions to Rational Equations--Example 9 This is part of a collection of math examples that show how to use graphical techniques to solve rational equations. Note: The download is an image file.

Related Resources

To see additional resources on this topic, click on the Related Resources tab.

Create a Slide Show

Subscribers can use Slide Show Creator to create a slide show from the complete collection of math examples on this topic. To see the complete clip art collection, click on this Link. To learn more about Slide Show Creator, click on this Link: 

Accessibility

This resource can also be used with a screen reader. 		Rational Functions and Equations
Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 1 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 1 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 1

Topic

Linear Functions

Description

This example demonstrates the process of converting a linear equation from standard form to slope-intercept form. The equation 2x + 4y = 8 is solved step-by-step, isolating y and dividing by its coefficient. The result is y = -1/2 x + 2, clearly showing the slope and y-intercept of the line.

 Standard Form
Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 10 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 10 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 10

Topic

Linear Functions

Description

This example illustrates the conversion of the linear equation x + y = 1 from standard form to slope-intercept form. The process involves isolating y, resulting in y = -x + 1. This simple transformation clearly reveals the slope and y-intercept of the line.

 Standard Form
Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 11 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 11 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 11

Topic

Linear Functions

Description

This example showcases the transformation of the linear equation x + y = -1 from standard form to slope-intercept form. The process involves isolating y, resulting in y = -x - 1. 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 12 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 12 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 12

Topic

Linear Functions

Description

This example demonstrates the conversion of the linear equation x - y = 1 from standard form to slope-intercept form. The solution process involves isolating y and changing the sign of both sides, resulting in y = x - 1. 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 13 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 13 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 13

Topic

Linear Functions

Description

This example illustrates the process of converting the linear equation -x + y = 1 from standard form to slope-intercept form. The solution involves rearranging the equation to isolate y, resulting in y = x + 1. 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 14 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 14 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 14

Topic

Linear Functions

Description

This example demonstrates the conversion of the linear equation -x - y = -1 from standard form to slope-intercept form. The process involves manipulating the equation to solve for y, yielding y = -x + 1. 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 15 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 15 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 15

Topic

Linear Functions

Description

This example showcases the transformation of the linear equation -x - y = 1 from standard form to slope-intercept form. The solution process involves isolating y, resulting in y = -x - 1. 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 16 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 16 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 16

Topic

Linear Functions

Description

This example demonstrates the conversion of the linear equation -x + y = -1 from standard form to slope-intercept form. The process involves isolating y, resulting in y = x - 1. This transformation clearly reveals the slope and y-intercept of the line.

Linear functions are fundamental mathematical concepts that describe relationships between two variables. The examples in this collection, such as showing step-by-step transformations from standard form to slope-intercept form, help in understanding how each part of the equation affects the graph and the relationship itself.

 Standard Form
Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 17 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 17 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 17

Topic

Linear Functions

Description

This example illustrates the conversion of the linear equation x - y = -1 from standard form to slope-intercept form. The solution involves isolating y, resulting in y = x + 1. 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 18 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 18 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 18

Topic

Linear Functions

Description

This example demonstrates the conversion of the linear equation -x - y = 1 from standard form to slope-intercept form. The process involves rearranging the equation to isolate y, resulting in y = -x - 1. 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 19 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 19 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 19

Topic

Linear Functions

Description

This example illustrates the conversion of the linear equation 12x + 28y = 0 from standard form to slope-intercept form. The solution involves isolating y and dividing by its coefficient, resulting in y = -3/7 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 2 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 2 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 2

Topic

Linear Functions

Description

This example illustrates the conversion of the linear equation 3x + 6y = -18 from standard form to slope-intercept form. The solution involves isolating y and dividing by its coefficient, resulting in y = -1/2 x - 3. 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 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