My book has given me the following
Given are the lines $k$: $y = ax + 6$ and $l$: $y= \frac{1}{2}ax +3a$. For which $a$ do the lines $k$ and $l$ cross each other on the y-axis?
I've tried resolving this one but the ax is confusing me a lot, should I be reading $y = a \times x+6$ or is it actually $ax+6$? I'm thinking that the first thing I said was true, if it was, how would we go about calculating the $x$ in this formula?
The answer to the question is: $2$ but why? Can someone maybe explain what's going on here? I can't seem to figure this one out. Links to tutorials or resources where these subjects are explained would be greatly appreciated!
HINT
Two curves $y = ax+6$ and $y = ax/2 + 3a$ cross when they hit same $y$ and same $x$. so you have $$ ax+6 = y = ax/2 + 3a $$ Since they cross on the $y$-axis, any point there has coordinates $(0,y)$, so $x=0$, which leaves you to plug that into the above equation and find both $y$ and $a$. Can you do that?