Exercise 52 Page 152

An equation in slope-intercept form follows a specific format. y= mx+b For an equation in this form, m is the slope and b is the y-intercept. We are given six points, however, to write a linear equation we only need two. Let's choose the points that we will use. (1,5) and (2,8)To calculate m, we will start by substituting the points into the Slope Formula.

m=y_2-y_1/x_2-x_1

SubstitutePoints

Substitute ( 1,5) & ( 2,8)

m=8- 5/2- 1

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Simplify right-hand side

SubTerms

Subtract terms

m=3/1

DivByOne

a/1=a

m=3

A slope of 3 means that for every 1 horizontal step in the positive direction, we take 3 vertical steps in the positive direction. Now that we know the slope, we can write a partial version of the equation. y= 3 x+b To complete the equation, we also need to determine the y-intercept, b. Since we know that the given points will satisfy the equation, we can substitute one of them into the equation to solve for b. Let's use ( 1, 5).

y=3x+b

SubstituteII

x= 1, y= 5

5=3( 1)+b

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Solve for b

IdPropMult

Identity Property of Multiplication

5=3+b

SubEqn

LHS-3=RHS-3

2=b

RearrangeEqn

Rearrange equation

b=2

A y-intercept of 2 means that the line crosses the y-axis at the point (0,2). We can now complete the equation. y= 3x+2 This corresponds to option G.