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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

Practice Test

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Exercise 3 Page 192

What do m and b represent in the slope-intercept form?

Slope: 14
y-intercept: 72

Equations in slope-intercept form follow a specific format, where m represents the slope of the line and b is the y-intercept. y= mx+ bLet's rewrite our equation a little bit so that it more closely resembles this format. This will make it easier to identify the features of the equation.

- 1/2x+2y=7

LHS+1/2x=RHS+1/2x

- 1/2x+2y+1/2x=7+1/2x

CommutativePropAdd

Commutative Property of Addition

2y+1/2x-1/2x=1/2x+7

Subtract term

2y=1/2x+7

.LHS /2.=.RHS /2.

2y/2=12x+7/2

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Simplify left-hand side

MovePartNumRight

a* b/c=a/c* b

2/2y=12x+7/2

Calculate quotient

1y=12x+7/2

Identity Property of Multiplication

y=12x+7/2

▼

Simplify right-hand side

Write as a sum of fractions

y=12x/2+7/2

a/b=1/b* a

y=1/2(1/2)x+7/2

Multiply fractions

y=1(1)/2(2)x+7/2

Identity Property of Multiplication

y=1/2(2)x+7/2

Multiply

y=1/4x+7/2

The given equation is now in the slope-intercept form. Below we have highlighted the slope m and y-intercept b. y= 1/4x+ 7/2 We can see that the slope is 14 and the y-intercept is 72.

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