Given the equation of the line and point P not on the line, find the equation of a line parallel to the given line and a line pe
rpendicular to the given line through the given point; y= -3x + 7; P(2,-4)
1 answer:
Answer:
y = -3x + 2; y = ⅓x -14/3
Step-by-step explanation:
Step 1. Find the equation of the parallel line
Original line: y = -3x+ 7
Parallel line: slope = m₁ = -3
The line passes through (2, -4).
y = m₁x + b Insert the values
-4 = (-3)×2 + b
-4 = -6 + b Add 6 to each side
b = 2
y = -3x + 2
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Step 2. Find the slope (m₂) of the perpendicular line
m₂ = -1/m₁ Substitute the value of m₁
m₂ = -1/(-3)
m₂ = ⅓
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Step 3. Find the equation for the perpendicular line
y = mx + b
y = ⅓x + b
The line passes through (2, -4).
-4 = ⅓(2) + b Substitute the values
-4 = ⅔ + b Subtract ⅔ from each side
-4 - ⅔ = b
b = -14/3
y = ⅓x - 14/3
In the image, below the graph of your original equation is the red line.
The green line passing through (2, -4) is the parallel line.
The purple line passing through (2, -4) is the perpendicular to both lines.
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