The rise would have to be 12.
This is because in order to be "Similar" triangles the sides need to be proportionate.
(1/3 = 4/12)
That's is depend from the author of the equation. But most time there is need to multiply value X into constant before.
In other words it look likes
y=2*x-3
Let's say we're at the store and you want to buy 10 boxes of cookies for a party. Each box of cookies cost 4.89(counting tax), you don't know if you have enough money to buy the cookies with the $65.00 you have with you. You could round the price up to $5.00 and do more simple multiplication. Your total would estimate about $50.00. Now you know you have more than enough money to buy cookies. I hope that makes sense. :)
Direct variation: y=kx where k is some number thats not 0
that means if x is 2, y is 2k. if x is 1, y is k. if x is 0, y is 0.
notice: no matter what k is, when you put 0 in for x, y will always be 0. that means that a direct variation always goes through the origin, a.k.a. (0,0).
do all lines go through the origin? nah. a line is y=mx+b, where m and b are some numbers. a line is only a direct variation if b is 0. this makes sense because if b is 0, then the y-intercept is 0, so the line goes through the origin.
in conclusion, no, not all linear relationships are direct varations, but all direct variations are linear relationships.
