Question

If the straight lines $\frac{y}{2}=x-p$ and $ax+5=3y$ are parallel, then find $a$.

Answer 1

Find the slope of the first line,

$\begin{array}{c}\frac{y}{2}=x-p\\ \frac{dy}{dx}\times \frac{1}{2}=1\\ \frac{dy}{dx}=2\end{array}$

Find the slope of the second line,

$\begin{array}{c}ax+5=3y\\ a=3\frac{dy}{dx}\\ \frac{dy}{dx}=\frac{a}{3}\end{array}$

If the lines are parallel then their slopes must be equal.

So,

$\begin{array}{c}\frac{a}{3}=2\\ a=6\end{array}$