Exercise 41 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 ( 0,1) & ( - 2,4)

m=4- 1/- 2- 0

SubTerms

Subtract terms

m=3/- 2

MoveNegDenomToFrac

Put minus sign in front of fraction

m=- 3/2

A slope of - 32 means that for every 2 horizontal steps in the negative 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= - 3/2 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, 1), 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= - 3/2x+ 1