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Big Ideas Math: Modeling Real Life, Grade 8

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Big Ideas Math: Modeling Real Life, Grade 8 View details

6. Writing Equations in Slope-Intercept Form

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Exercise 3 Page 177

Apply inverse operations to isolate y and write the linear equation in slope-intercept form.

y=1/3x-7/2

Practice makes perfect

An equation in slope-intercept form follows a specific format. y= mx+ bTo write the given linear equation in slope-intercept form, we will use the Properties of Equality to apply inverse operations on the equation and isolate y. Remember, only like terms can be combined.

- 2/3x+2y=- 7

LHS+2/3x=RHS+2/3x

- 2/3+2y+2/3x=- 7+ 2/3x

CommutativePropAdd

Commutative Property of Addition

2y- 2/3x+2/3x=2/3x- 7

Subtract term

2y=2/3x-7

Now, we can use the Division Property of Equality to simplify the equation even further.

2y=2/3x-7

.LHS /2.=.RHS /2.

2y/2=23x-7/2

▼

Simplify left-hand side

MovePartNumRight

a* b/c=a/c* b

2/2y=23x-7/2

Calculate quotient

1y=23x-7/2

Identity Property of Multiplication

y=23x-7/2

▼

Simplify right-hand side

Write as a difference of fractions

y=23x/2-7/2

a/b=1/b* a

y=1/2(2/3)x-7/2

Multiply fractions

y=1(2)/2(3)x-7/2

CancelCommonFac

Cancel out common factors

y=1(2)/2(3)x-7/2

Simplify quotient

y=1/3x-7/2

Subchapter links

Try It p.174-175

Self-Assessment for Concepts & Skills p.175

Self-Assessment for Problem Solving p.176

Review & Refresh p.177

Concepts, Skills, & Problem Solving p.177-178