Exercise 8 Page 184

Let's start by expressing f(-1)=-6 as (-1,-6), and f(4)=- 6 as (4,- 6). 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. Here, we are given that the line passes through two known points. (-1,-6) and (4, - 6) To determine the slope of the line, we use the Slope Formula.

m=y_2-y_1/x_2-x_1

SubstitutePoints

Substitute ( - 1,-6) & ( 4,- 6)

m=- 6-( -6)/4-( - 1)

SubNeg

a-(- b)=a+b

m=- 6+6/4+1

AddTerms

Add terms

m=0/5

CalcQuot

Calculate quotient

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, -6).

y-y_1=m(x-x_1)

SubstituteValues

Substitute values

y-( -6)= 0(x-( - 1))

ZeroPropMult

Zero Property of Multiplication

y-(-6)= 0

SubNeg

a-(- b)=a+b

y + 6 = 0

SubEqn

LHS-6=RHS-6

y = - 6

Now, we can write the equation in terms of f(x). f(x) = - 6 Please note that if we substitute any point of the line into the point-slope equation, we will get the same answer, since the slope is 0.