Question

Find the equation of the line that passes through (1, -2) and is perpendicular
to the line joining the points (4, 2) and (-1, 7).

O y = -x - 3
O y = -x + 3
O y = -x + 6
O y = x - 3

Answer 1

Answer:

D. y = x - 3

Step-by-step explanation:

First, find the slope (m) of the line it is perpendicular to using the points of the line, (4, 2) and (-1, 7):

$slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{7 - 2}{-1 - 4} = \frac{5}{-5} = -1$

Thus, the slope (m) of the line that is perpendicular to the line that runs through (4, 2) and (-1, 7) would be the negative reciprocal of -1.

The slope (m) if the line that is perpendicular to the other line = 1

Thus, substitute m = 1 and (a, b) = (1, -2) into y - b = m(x - a)

y - (-2) = 1(x - 1)

y + 2 = x - 1

Subtract 2 from both sides

y = x - 1 - 2

y = x - 3