Exercise 5 Page 167

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,-2) & ( 4,10)

m=10-( -2)/4- 0

▼

Evaluate right-hand side

SubNeg

a-(- b)=a+b

m=10+2/4-0

AddSubTerms

Add and subtract terms

m=12/4

CalcQuot

Calculate quotient

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= 3x+ b To complete the equation, we also need to determine the y-intercept, b. Since we know that one of the given points is (0, -2), we know that we have a y-intercept of -2. We can now complete the equation. y= 3x+( -2) ⇒ y=3x-2