Exercise 42 Page 190

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. We can calculate the slope by substituting only two points of the given table into the Slope Formula.

m = y_2-y_1/x_2-x_1

SubstitutePoints

Substitute ( 0,-3) & ( 1,- 1)

m=- 1-( - 3)/1- 0

▼

Simplify right-hand side

SubNeg

a-(- b)=a+b

m=- 1+3/1-0

AddSubTerms

Add and subtract terms

m=2/1

DivByOne

a/1=a

m= 2

A slope of 2 means that for every 1 horizontal step in the positive direction, we take 2 vertical steps in the positive direction. Now that we know the slope, we can write a partial version of the equation. y= 2 x+ b To complete the equation, we also need to substitute the y-intercept, b. We can see that one of our given points, (0, - 3), 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= 2x+( - 3) → y=2x-3