Exercise 7 Page 157

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. Let's use the given points 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 ( 8,2) & ( - 8,6)

m=6- 2/- 8- 8

SubTerms

Subtract terms

m=4/- 16

MoveNegDenomToFrac

Put minus sign in front of fraction

m = - 4/16

ReduceFrac

a/b=.a /4./.b /4.

m = - 1/4

A slope of - 14 means that for every 4 horizontal steps in the positive direction, we take 1 vertical step in the negative direction. Now that we know the slope, we can write a partial version of the equation. y= - 1/4 x+ b To determine the y-intercept b, we can substitute one of the points into the equation and solve for b. Let's use ( 8, 2).

y=- 1/4x+b

SubstituteII

x= 8, y= 2

2=- 1/4( 8)+b

▼

Solve for b

MoveRightFacToNumOne

1/b* a = a/b

2 = - 8/4 + b

CalcQuot

Calculate quotient

2 = - 2 + b

AddEqn

LHS+2=RHS+2

4 = b

RearrangeEqn

Rearrange equation

b = 4

A y-intercept of 4 means that the line crosses the y-axis at the point (0, 4).