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Answer:
y = ½(13- x)
Step-by-step explanation:
Step 1. Find the<em> slope (m₁) of the original line </em>
The equation for the original line is
y = 2x - 6
slope = m₁ = 2
Step 2. Find the <em>slope (m₂) of the perpendicular line </em>
m₂ = -1/m₁ Substitute the value of m₁
m₂ = -1/2
Step 3. Find the <em>equation for the perpendicular line</em>
y = mx + b Substitute the value of m₂
y = -½x + b
The line passes through (5, 4).
4 = -½(5) + b Add 5/2 to each side
4 = -5/2 + b Add 2 to each side
b = 13/2
y = -½x + 13/2
y = ½(13 – x)
In the image, below, the red line is the graph of your original equation.
The blue line passing through (5, 4) is the perpendicular line.
