Exercise 14 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 ( 2,7) & ( 0,-5)

m=-5- 7/0- 2

▼

Evaluate right-hand side

SubTerms

Subtract terms

m=-12/-2

DivNegNeg

- a/- b=a/b

m=12/2

CalcQuot

Calculate quotient

m= 6

A slope of 6 means that for every 1 horizontal step in the positive direction, we take 6 vertical steps in the positive direction. Now that we know the slope, we can write a partial version of the equation. y= 6x+ 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= 6x+( -5) ⇒ y=6x-5