# Thread: Find the intersections of the lines

1. ## Find the intersections of the lines

l : 3x+4y =5 and m: (x,y) = (2, -4) + t(2,6)

So, I was thinking i could turn m into slope form, like l is..

so I think m: (x,y) = (2, -4) + t(2,6) is also y = 3x - 10

and then I just find where they are equal? or use system of linear equations and substitute?

2. Originally Posted by zodiacbrave
l : 3x+4y =5 and m: (x,y) = (2, -4) + t(2,6)

So, I was thinking i could turn m into slope form, like l is..

so I think m: (x,y) = (2, -4) + t(2,6) is also y = 3x - 10

and then I just find where they are equal? or use system of linear equations and substitute?
Use your parametric form in the general form. i.e. if $x = 2 + 2t$ and $y = -4 + 6t$ then

$3(2 + 2t ) + 4(-4 + 6t) = 5$ and solve for $t$. Once you have this, sub. back into your parametric form.

Spoiler:
$t = \frac{1}{2}$ and the point is $(3,-1)$