Answer:
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.
