Question

What is the solution for this problem?

Answer 1

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