### Home > AC > Chapter 12 > Lesson 12.4.3 > Problem12-94

12-94.

If $f\left(-1\right)=7$ and $f\left(3\right)=8$, and if the graph of $f\left(x\right)$ is a line:

1. Graph the line on graph paper.

$f\left(-1\right)=7$ represents the point $\left(-1,7\right)$.
Graph this point and the point corresponding to $f\left(3\right)=8$ in order to sketch the line.

2. Find the equation for $f\left(x\right)$.

Use the $y = mx + b$ format where $m=\text{slope}\left(\text{growth}\right)$ and $b=y\text{-intercept}\left(\text{starting point}\right)$.

Find the growth and substitute one of the coordinates of a point in the problem and solve for $b$.

3. If $g\left(x\right)$ is a line that is perpendicular to $f\left(x\right)$, what is its slope?

A line $g\left(x\right)$ that is perpendicular to $f\left(x\right)$ has a slope that is the negative reciprocal of the slope of the line $f\left(x\right)$.