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 = \frac{y _{2} - y _{1}}{x _{2} - x _{1}}

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

m = \frac{5 - 5}{- 1 - ( - 3 )}

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Simplify right-hand side

$a - (- b) = a + b$

m = \frac{5 - 5}{- 1 + 3}

Add and subtract terms

m = \frac{0}{2}

$\frac{a}{b} = a \cdot \frac{1}{b}$

m = 0 \cdot \frac{1}{2}

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})

Substitute values

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

Zero Property of Multiplication

y - 5 = 0

$LHS + 5 = RHS + 5$

y = 0 + 5

Identity Property of Addition

y = 5

We found a line

y = 5,

so the function we are asked for is

f (x) = 5 .

Exercise 66 Page 320

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