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

D) y = -x - 3

Step-by-step 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.