Q:

Algebraically find the value of $a$.

The graphs of $2y + x + 3 = 0\,$ and $3y + ax + 2 = 0\,$ meet at right angles. Algebraically find the value of $a$.
My instinct was making the two equations equal each other and solve like so:

$2y + x + 3 \, = 3y + ax + 2\,$
$-y + x + 1 \, = ax\,$
$\displaystyle \frac{-y + x + 1}{x}  = \frac{ax}{x}\,$
$\displaystyle \frac{-y + x + 1}{x} \, = a\,$

I noticed my problem mentions the equations meeting at right angles. Would I need to change my equation for the correct answer; do I add the two equations and set them equal to 90?

A:

The first line is 
$$y=-\frac12 x -\frac32$$
The slope is $-\frac12$. To be perpendicular, the slope of the second line is $2$. 
Using that, you should be able to recover $a$.

