Exercise 66 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) = 5 and f(- 1) = 5. This means that the linear function passes through two known points. (- 3,5) and (- 1, 5) To determine the slope of the line, we use the Slope Formula.

m = y_2-y_1/x_2-x_1

SubstitutePoints

Substitute ( - 3, 5) & ( - 1, 5)

m = 5- 5/- 1-( - 3)

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Simplify right-hand side

SubNeg

a-(- b)=a+b

m = 5-5/- 1 + 3

AddSubTerms

Add and subtract terms

m = 0/2

MoveNumLeft

a/b=a* 1/b

m = 0 * 1/2

ZeroPropMult

Zero Property of Multiplication

m = 0

Now that we know the slope of the line is 0, 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 ( - 1, 5).

y - y_1 = m(x - x_1)

SubstituteValues

Substitute values

y - 5 = 0(x - ( - 1))

ZeroPropMult

Zero Property of Multiplication

y - 5 = 0

AddEqn

LHS+5=RHS+5

y = 0 + 5

IdPropAdd

Identity Property of Addition

y = 5

We found a line y=5, so the function we are asked for is f(x) = 5.