Exercise 16 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 ( -6,0) & ( 0,-24)

m=-24- 0/0-( -6)

▼

Evaluate right-hand side

SubNeg

a-(- b)=a+b

m=-24-0/0+6

AddSubTerms

Add and subtract terms

m=-24/6

CalcQuot

Calculate quotient

m= - 4

A slope of - 4 means that for every 1 horizontal step in the positive direction, we take 4 vertical steps in the negative direction. Now that we know the slope, we can write a partial version of the equation. y= -4x+ b To complete the equation, we also need to substitute the y-intercept, b. We can see that one of our given points, (0, - 24), 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= -4x+( -24) ⇒ y=-4x-24