###### Example6.5.2

Rewrite $$4x-2y=10$$ in slope-intercept form.

In being asked to rewrite this equation in slope-intercept form, we're really being asked to solve the equation $$4x-2y=10$$ for $$y\text{.}$$

\begin{align*} 7x-2y \amp= 10 \\ 7x-2y \highlight{{}-7x} \amp= 10\highlight{{}-7x} \\ -2y \amp= -7x + 10 \\ \frac{-2y}{\highlight{-2}} \amp= \frac{-7x + 10}{\highlight{-2}} \\ y \amp= -\frac{7}{2}x -5 \end{align*}

In the final step of work, we divided each term on the right side of the equation by $$-2\text{.}$$

This is an example of polynomial division that we have already done. We'll extend it to more complicated examples, many of which involve dividing polynomials by variables (instead of just numbers).

in-context