Find the Equation Using Two Points f(-2)=1 , g(-2)=-2

$f (- 2) = 1$ , $g (- 2) = - 2$

Step 1

$f (- 2) = 1$ , which means $(- 2, 1)$ is a point on the line. $g (- 2) = - 2$ , which means $(- 2, - 2)$ is a point on the line, too.

$(- 2, 1), (- 2, - 2)$

Step 2

Find the slope of the line between $(- 2, 1)$ and $(- 2, - 2)$ using $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ , which is the change of $y$ over the change of $x$ .

Slope is equal to the change in $y$ over the change in $x$ , or rise over run.

$m = \frac{change in y}{change in x}$

The change in $x$ is equal to the difference in x-coordinates (also called run), and the change in $y$ is equal to the difference in y-coordinates (also called rise).

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

Substitute in the values of $x$ and $y$ into the equation to find the slope.

$m = \frac{- 2 - (1)}{- 2 - (- 2)}$

Simplify.

Multiply $- 1$ by $- 2$ .

$\frac{- 2 - (1)}{- 2 + 2}$

Add $- 2$ and $2$ .

$\frac{- 2 - (1)}{0}$

The expression contains a division by $0$ . The expression is undefined.

Undefined

Step 3

The slope of the line is undefined, which means that it is perpendicular to the x-axis at $x = - 2$ .

$x = - 2$

Step 4

The final answer is the equation in slope-intercept form.

$y = - 2$

Step 5

Replace $y$ by $f (x)$ .

$f (x) = - 2$

Step 6

Find the Equation Using Two Points f(-2)=1 , g(-2)=-2

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