What is the standard form of a line that goes through (5,−4) and is perpendicular to y=5/4x−5?

lascieflYr

lascieflYr

Answered question

2022-11-24

What is the standard form of a line that goes through (5,−4) and is perpendicular to y = 5 4 x - 5 ?

Answer & Explanation

Dillan Foley

Dillan Foley

Beginner2022-11-25Added 9 answers

Since the line is perpendicular to another line with slope 5 4 , its slope will be the negative reciprocal of the other line's slope.
Hence the slope of the line is - 4 5 . We also know it passes through (5,−4).
Using
y=mx+c
we know
m (slope) = - 4 5
therefore
y = - 4 5 x + c
Substituting (5,−4) gives you
- 4 = - 4 5 ( 5 ) + c
c=0
Therefore
y = - 4 5 x
5y=−4x
5y+4x=0

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