Question

Identify an equation in point-alope form for the line perpendicular to y-x-7 that passes through (-2,-6).​

Answer 1

Answer:

$y + 6 = -1(x + 2).$

Step-by-step explanation:

Let's find the general equation of the given line:

$y - x - 7 = 0\\\\y = x + 7.$

We can see that $m = 1.$

Thus, the slope of any perpendicular line to the line $y = x + 7$ is $-1.$

Given that the perpendicular line passes through (-2, -6), its point-slope form equation is as given:

$y - y_1 = m(x - x_1)\\\\y - (-6) = -1(x - (-2))\\\\y + 6 = -1(x + 2).$