You got the gradient right, because to find a perpendicular gradient, you divide -1 by the original gradient.

If you know a line has gradient g and passes through (x,y), then its y-intercept is y - (g*x).

For your one, it passes through (4,7) and has a gradient of 3/2, so the y-intercept is 7 - (3/2*4) = 1.