Describing Inverses of Functions

To algebraically determine the inverse of the given relation, we exchange $x$ and $y$ and solve for $y.$ $$\begin{array}{c}y=3-7x\stackrel{\text{switch}}{⟶}x=3-7y\end{array}$$ The result of isolating $y$ in the new equation will be the inverse of the given relation. Now we have the inverse of the given function. $$\begin{array}{c}y=\frac{3-x}{7}\end{array}$$

Graphing the Inverse Relation

To graph the inverse linear relation, we will proceed in the same way. Let's first write it in slope-intercept form. $$\begin{array}{c}y=\frac{3-x}{7}\iff y=\text{-}\frac{1}{7}x+\frac{3}{7}\end{array}$$ Finally, we can graph the inverse of the function as we graphed the function.