Question

what is an equation of the line that passes through the point (-2,5) and is perpinduclar to the line whose equation is y= 1/2x +5

Answer 1

If you are asking for the line which passes through (-2,5) and is perpendicular to y=1/2(x) + 5 then the method is as follows.

1) Note that the gradient of y = 1/2(x) + 5 is 1/2. It is the number before the x.

2) Two perpendicular lines have gradients which multiply to give -1, so let 1/2m = -1. Then m = -2

3) Substitute into the following equation:
y - b = m(x - a), for a line with gradient m, passing through (a,b).

y - (5) = -2(x - (-2))

y - 5 = -2x - 4

y = -2x + 1