Exercise 6 Page 167

In this case, we are asked to write our equation in function notation. g(x)= mx+ b For an equation in this form, m is the slope and b is the y-intercept. We have also been given two points in function notation. To write these points as coordinate pairs, remember that the input x is the x-coordinate and the output g(x) is the y-coordinate. g( x)= y ⇔ ( x, y) g( 0)= 9 ⇔ ( 0, 9) g( 8)= 7 ⇔ ( 8, 7) 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 ( 0,9) & ( 8,7)

m=7-9/8-

▼

Evaluate right-hand side

SubTerms

Subtract terms

m=-2/8

ReduceFrac

a/b=.a /2./.b /2.

m=-1/4

MoveNegNumToFrac

Put minus sign in front of fraction

m= -1/4

A slope of - 14 means that for every 4 horizontal steps in the positive direction, we take 1 vertical step in the negative direction. Now that we know the slope, we can write a partial version of the equation. g(x)= -1/4x+ b To complete the equation, we also need to determine the y-intercept, b. We can see that one of our given points, (0, 9), 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. g(x)= -1/4x+ 9