I am given the area. I also know the slope.

The line is supposed start at 0,0.

I need to know the y coordinate.

I promise this isn't for homework.

Frankly this doesn't make much sense! You say "I am given the area". The area of

what? You say "I also know the slope". The slope of

what.

I can

guess that you have a line passing through (0, 0), with given slope m, and you want to find the (X, Y) coordinates of another point on that line such that the area of the triangle under the line, the triangle with vertices (0, 0), (X, Y), and (X, 0) is some given number A. The line with slope m, through (0, 0), has equation y= mx. The point with x= X is (X, mX) so the "height" of the triangle is mX, the "base" is X, and the area is "one half height time base", [tex](1/2)(mX)(X)= \frac{m}{2}X^2= A[/tex] to solve that for X, multiply both sides by 2 and divide by m to get [tex]X^2= \frac{2A}{m}[/tex]. Finally, take the square root of both sides- [tex]X= \sqrt{\frac{2A}{m}}[/tex]. And then [tex]Y= mX= m\sqrt{\frac{2A}{m}}= \sqrt{2mA}[/tex].