Exercise 65 Page 320

Equations in point-slope form follow a specific format. y- y_1= m(x- x_1) In this form, m is the slope of the line and ( x_1, y_1) is a point on the line. We are looking for a function with values f(- 2) = 0 and f(6) = - 4. This means that the linear function passes through two known points. (- 2, 0) and (6, - 4) To determine the slope of the line, we use the Slope Formula.

m = y_2-y_1/x_2-x_1

SubstitutePoints

Substitute ( - 2, 0) & ( 6, - 4)

m = - 4- 0/6-( - 2)

▼

Simplify right-hand side

SubNeg

a-(- b)=a+b

m = - 4 - 0/6 + 2

AddSubTerms

Add and subtract terms

m = - 4/8

ReduceFrac

a/b=.a /4./.b /4.

m = - 1/2

MoveNegNumToFrac

Put minus sign in front of fraction

m = - 1/2

Now that we know the slope of the line is - 12, we can write the equation of the line in point-slope form. We can use either of the given points as (x_1,y_1) in our equation. Let's use ( - 2, 0).

y - y_1 = m(x - x_1)

SubstituteValues

Substitute values

y - 0 = -1/2(x - ( - 2))

SubNeg

a-(- b)=a+b

y - 0 = -1/2(x+2)

Distr

Distribute -1/2

y - 0 = -1/2x - 1

IdPropAdd

Identity Property of Addition

y = -1/2x - 1

We found a line y=- 12x-1, so the function we are asked for is f(x) = - 12x-1.