Question

Write an equation of the line that is perpendicular to -x + y = 5 and passes through the point (2, -5). A) y = x - 7 B) y = x - 5 C) y = x - 3 D) y = -x - 3

Answer 1

D) y = -x - 3

Explanation:

Step 1. Find the slope (m₁) of the original line

The equation for the original line is

-x + y = 5 Add x to each side

y = x + 5

slope = m₁ = 1

Step 2. Find the slope (m₂) of the perpendicular line

m₂ = -1/m₁ Substitute the value of m₁

m₂ = -1/1

m₂ = -1

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Step 3. Find the equation for the perpendicular line

y = mx + b Substitute the value of m₂

y = -x + b

The line passes through (2, -5).

-5 = -2 + b Add 2 to each side

b = -3

y = -x - 3

In the image, below the graph of your original equation is the red line.

The blue line passing through (2, -5) is the perpendicular line.