SOLUTION: Write an equation of the line passing through the point (-2,1) and the perpendicular to the line y=2x-5

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Question 1160030: Write an equation of the line passing through the point (-2,1) and the perpendicular to the line y=2x-5
Found 2 solutions by greenestamps, MathLover1:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The equation of the given line is y=2x-5; its slope is 2.

The slope of a line perpendicular to the given line is the negative reciprocal of 2, which is -1/2.

The equation of the line is of the form y = (-1/2)x+c for some constant c. Find the value of c using the coordinates of the given point.

y+=+%28-1%2F2%29x%2Bc
1+=+%28-1%2F2%29%28-2%29%2Bc
1+=+1%2Bc
c+=+0

The equation of the line is y = (-1/2)x+0, or just y = (-1/2)x.

A graph of the given line (red) and the perpendicular line (green):

graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C2x-5%2C%28-1%2F2%29x%29

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

an equation of the line passing through the point (-2,1) and the perpendicular to the line y=2x-5
will be: use point-slope formula
y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is a slope, x%5B1%5Dand y%5B1%5D coordinates of given point
since this line is perpendicular to the line y=2x-5 whose slope is 2, your line will have a slope negative reciprocal which is -1%2F2
so
y-1=-%281%2F2%29%28x-%28-2%29%29
y-1=-%281%2F2%29%28x%2B2%29
y-1=-%281%2F2%29x-%281%2F2%29%282%29
y-1=-%281%2F2%29x-1
y=-%281%2F2%29x-1%2B1
y=-%281%2F2%29x-> your answer