Question

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What is the equation of a line that is perpendicular to y=4x+5 and passes through the point (8, 3)?
A. y=-1/4x-8
B. y=1/4x-8
C. y=-1/4x+5
D. y=-1/4x+3

Answer 1

so, what's the slope of y = 4x + 5?

Answer 2

Ok a line perpendicular to a line with slope m has slope -1/m

Answer 3

so if you answer Vocaloid's question you can get the slope of the line perpendicular to given line.

Answer 4

I will do a perpendicular and a parallel to show you how to do it...

First you need to put the equations in y = mx + b form
1. x - 5y = -10
-5y = -x - 10 (multiply the equation by -1)
5y = x + 10 (now divide by 5)
y = 1/5x + 2
Perpendicular lines have slopes that are the negative reciprocal. So the slope will be -5.
y - y1 = m(x - x1) using slope -5 and points (2,5)
y - 5 = -5(x - 2)
y - 5 = -5x + 10
y = -5x + 10 + 5
y = -5x + 15 (answer C)

2. 10x - 5y = 8
-5y = -10x + 8 (multiply by -1)
5y = 10x - 8 (divide by 5)
y = 2x -8/5
Parallel line have the same slope, so the slope will be 2.
y - y1 = m(x - x1) using slope 2 and points (2,4)
y - 4 = 2(x - 2)
y - 4 = 2x - 4
y = 2x - 4 + 4
y = 2x (answer E)

Answer 5

so the answer would be C y=1/4x+5

Answer 6

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