Question

Write an equation in point-slope form for the line that is perpendicular to the given line and passes through the given point.

Y - 3 = 4 (x + 2) through the point (- 2,6)

Answer 1

Answer: 4y + x - 22 = 0

Explanation:

Recall that for two lines to be perpendicular m1m2 = -1 ie, the product of their gradients must = -1

from the equation given, y - 3 = 4(x + 2), we need to rearrange it in the form

y = mx + c in order for us to ascertain the gradient.

y -3 = 4x + 8

y = 4x + 8 + 3

y = 4x + 11

Therefore, m1 = 4 while m2 = -1/4

The coordinate of the line = (-2, 6) . We now use this to find the value of c.

6 = -1/4 x -2 + c

6 = 1/2 + c

multiply by 2

12 = 1 + 2c

12 - 1 = 2c

11 = 2c

c = 11/2

now to find the equation of the second line

y = -x/4 + 11/2

now multiply through by 4

4y = -x + 22

4y + x - 22 = 0 is the required equation