Exercise 67 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(3) = - 1 and f(- 4) = - 15. This means that the linear function passes through two known points. (3, - 1) and (- 4, - 15) To determine the slope of the line, we use the Slope Formula.

m = y_2-y_1/x_2-x_1

SubstitutePoints

Substitute ( - 4, - 15) & ( 3, - 1)

m = - 1-( - 15)/3-( - 4)

▼

Simplify right-hand side

SubNeg

a-(- b)=a+b

m = - 1 + 15/3 + 4

AddSubTerms

Add and subtract terms

m = 14/7

CalcQuot

Calculate quotient

m = 2

Now that we know the slope of the line is 2, 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 ( 3, - 1).

y - y_1 = m(x - x_1)

SubstituteValues

Substitute values

y - ( - 1) = 2(x - 3)

Distr

Distribute 2

y - (- 1) = 2x- 6

SubNeg

a-(- b)=a+b

y + 1 = 2x - 6

SubEqn

LHS-1=RHS-1

y = 2x - 7

We found a line y = 2x - 7, so the function we are asked for is f(x) = 2x - 7.