Exercise 64 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) = 6 and f(-1) = - 3. This means that the linear function passes through two known points. (2,6) and (- 1, - 3) To determine the slope of the line, we use the Slope Formula.

m = y_2-y_1/x_2-x_1

SubstitutePoints

Substitute ( - 1, - 3) & ( 2, 6)

m = 6-( - 3)/2-( - 1)

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Simplify right-hand side

SubNeg

a-(- b)=a+b

m = 6+3/2+1

AddTerms

Add terms

m = 9/3

CalcQuot

Calculate quotient

m = 3

Now that we know the slope of the line is 3, 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, 6).

y - y_1 = m(x - x_1)

SubstituteValues

Substitute values

y - 6 = 3(x - 2)

Distr

Distribute 3

y - 6 = 3x - 6

AddEqn

LHS+6=RHS+6

y = 3x

We found a line y=3x, so the function we are asked for is f(x) = 3x.