Calculate $a$ when the lines cross

Question

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!

Please use MathJax to format your posts. – gen-ℤ ready to perish Sep 20 '17 at 21:57 — gen-ℤ ready to perish, Sep 20 '17 at 21:57
@BDN I'm sorry, under which tag would this better fit? – Jordy Sep 20 '17 at 22:05 — Jordy, Sep 20 '17 at 22:05
graphing-functions, I've suggested an edit – BDN Sep 20 '17 at 22:05 — BDN, Sep 20 '17 at 22:05

score 3 · Accepted Answer · answered Sep 20 '17 at 22:01

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?

Calculate $a$ when the lines cross

1 Answers1