Exercise 15 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,-4) & ( 0,-4)

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

▼

Evaluate right-hand side

SubNeg

a-(- b)=a+b

m=-4+4/0-2

AddSubTerms

Add and subtract terms

m=0/-2

CalcQuot

Calculate quotient

m=0

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