Find the equation of the line that passes through (−2,1) and is perpendicular to the line that passes through the following points: (1,4),(−2,3)

Paula Cameron

Paula Cameron

Answered question

2022-11-08

Find the equation of the line that passes through (−2,1) and is perpendicular to the line that passes through the following points: (1,4),(−2,3)

Answer & Explanation

x713x9o7r

x713x9o7r

Beginner2022-11-09Added 15 answers

Slope of the line through (1,4) and (−2,3) is given by:
m = y 2 - y 1 x 2 - x 1 = 3 - 4 ( - 2 ) - 1 = - 1 - 3 = 1 3
If the slope of a line is m, lines perpendicular to it have slope - 1 m . In this case, the slope of the perpendicular lines will be −3.
The form of a line is y=mx+c where c is the y-intercept, so if we substitute in −3 as the slope and the given points (−2,1) for x and y, we can solve to find the value of c:
1=−3(−2)+c
c=−5
So the equation of the line we want is y=−3x−5

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