Question

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

Answer 1

Answer:

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

Step-by-step explanation:

Given

Perpendicular to: y = x - 7

Passes through (-2,-6)

Required

Find the equation

An equation has the form:

$y = mx + b$

Where

$m = slope$

In $y = x - 7$

$m = 1$

Since the required equation is perpendicular to $y = x - 7$, then the relationship between their slopes is:

$m_2 = -\frac{1}{m}$

Substitute 1 for m

$m_2 = -\frac{1}{1}$

$m_2 = -1$

The equation is then calculated using:

$y -y_1 = m(x - x_1)$

Where

$m_2 = -1$

$(x_1,y_1) = (-2,-6)$

So, we have:

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

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

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