Equation of a straight line in the treated segments Problem: $$4x - 7y -2  = 0$$
But the real problem is that in my math book, the result of this is different than my solution.
This is my progress so far:
$$4x - 7y - 2 = 0$$
$$\frac{4x}{2} - \frac{7y}{2} = 1$$
This is result that should be:
$$
\frac{x}{1/2} + \frac{y}{-2/7} = 1
$$
My question is how this is possible?

Starting from
$$\frac{4x}{2} - \frac{7y}{2} = 1$$
recognize that you can simplify the fraction in the first term since ${4}/{2}={2}/{1}$
$$\frac{2x}{1} - \frac{7y}{2} = 1$$
then observe that $z=\frac{1}{1/z}$ for any $z\neq 0$. Also, $\frac{1}{a/b}=\frac{b}{a}$ if both $a\ne 0$ and $b\ne 0$. This allows you to conclude that
$$\frac{2}{1}=\frac{1}{\frac{1}{2/1}}=\frac{1}{{1}/{2}}$$
$$\frac{7}{2}=\frac{1}{\frac{1}{7/2}}=\frac{1}{{2}/{7}}$$
therefore
$$\frac{2x}{1} - \frac{7y}{2} = \frac{x}{1/2} - \frac{y}{2/7} = \frac{x}{1/2} + \frac{y}{-2/7}=1$$
