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Find the equation of a line that passes through the point (4,2) that is perpendicular to the line y=4/3x

User Bryan Massoth
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1 Answer

19 votes
19 votes

Answer:

Explanation:

The a line that is perpendicular to the reference line will have a slope that is the negative inverse of the slope of the reference line. We'll look for a line that has the form y=mx+b, where m is the slope and b is the y-intercept. The reference line y=(4/3)x has a slope of (4/3) and a y-intercept of 0 (it crosses the y axis at x = 0).

The negative inverse the the slope (4/3) would be -(3/4).

The new line will be y = -(3/4)x + b.

To find point, use the given point and solve for b:

y = -(3/4)x + b

y = -(3/4)x + b for point (4,2)

2= -(3/4)(4) + b

2= -3 + b

b = 5

The equation of the perpendicualr line is y = -(3/4)x + 5

See attached graph.

Find the equation of a line that passes through the point (4,2) that is perpendicular-example-1
User Tom
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