Exercise 17 Page 169

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 ( 0,5) & ( -1.5,1)

m=1- 5/-1.5- 0

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Evaluate right-hand side

SubTerms

Subtract terms

m=-4/-1.5

ReduceFrac

a/b=.a /(-0.5)./.b /(-0.5).

m=8/3

A slope of 83 means that for every 3 horizontal step in the positive direction, we take 8 vertical steps in the positive direction. Now that we know the slope, we can write a partial version of the equation. y= 83x+ b To complete the equation, we also need to substitute the y-intercept, b. We can see that one of our given points, (0, 5), lies on the y-axis. Since the line crosses the y-axis at this point, we know the y-intercept and can complete the equation. y= 8/3x+ 5