in general you need to get the three intersecting points and calculate the side length of each side.
in this case, it's a little special that one side lies with x-axis and y=x intersects it at (0,0) so you can find the other two intersecting points easily
by sovling y=x 4x+5y = 15 => (x = 5/3, y = 5/3)
and y = 0 4x+5y=15 (x = 15/4, y = 0)
from this you know the base of the triangle is 15/4 and height is 5/3
so you can easily apply the basexheight/2 formula