First of all let's rearrange the equation for the given line:
4x + 7y + 3 = 0 7y = -4x - 3 y = (-4/7)x - 3/7 Now we know that the gradient of the line is -4/7
The gradients of two perpendicular lines multiply by each other to give -1, ie. (-4/7)*m = -1 m = -1/(-4/7) = 7/4, therefor the gradient of the perpendicular line is 7/4
Now we can substitute this and the point (-2, 1) into the equation y - y1 = m(x - x1) y - 1 = 7/4(x - (-2)) y = 7/4x + 7/2 + 1 y = 7/4x + 9/2
If we look at the given answers then C is correct, since 9/2 = 18/4 and so the equation may also be written as y = 7/4x + 18/4
