SOLUTION: Find an equation of the line that passes through the point (2,-7) and is perpendicular to the line 4x=y-8. please show steps

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Question 1048400: Find an equation of the line that passes through the point (2,-7) and is perpendicular to the line 4x=y-8.
please show steps
Found 2 solutions by MathLover1, ewatrrr:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

the line that passes through the point (2,-7) and is perpendicular to the line 4x=y-8->y=4x%2B8
Solved by pluggable solver: Finding the Equation of a Line Parallel or Perpendicular to a Given Line


Remember, any two perpendicular lines are negative reciprocals of each other. So if you're given the slope of 4, you can find the perpendicular slope by this formula:

m%5Bp%5D=-1%2Fm where m%5Bp%5D is the perpendicular slope


m%5Bp%5D=-1%2F%284%2F1%29 So plug in the given slope to find the perpendicular slope



m%5Bp%5D=%28-1%2F1%29%281%2F4%29 When you divide fractions, you multiply the first fraction (which is really 1%2F1) by the reciprocal of the second



m%5Bp%5D=-1%2F4 Multiply the fractions.


So the perpendicular slope is -1%2F4



So now we know the slope of the unknown line is -1%2F4 (its the negative reciprocal of 4 from the line y=4%2Ax%2B8). Also since the unknown line goes through (2,-7), we can find the equation by plugging in this info into the point-slope formula

Point-Slope Formula:

y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope and (x%5B1%5D,y%5B1%5D) is the given point



y%2B7=%28-1%2F4%29%2A%28x-2%29 Plug in m=-1%2F4, x%5B1%5D=2, and y%5B1%5D=-7



y%2B7=%28-1%2F4%29%2Ax%2B%281%2F4%29%282%29 Distribute -1%2F4



y%2B7=%28-1%2F4%29%2Ax%2B2%2F4 Multiply



y=%28-1%2F4%29%2Ax%2B2%2F4-7Subtract -7 from both sides to isolate y

y=%28-1%2F4%29%2Ax%2B2%2F4-28%2F4 Make into equivalent fractions with equal denominators



y=%28-1%2F4%29%2Ax-26%2F4 Combine the fractions



y=%28-1%2F4%29%2Ax-13%2F2 Reduce any fractions

So the equation of the line that is perpendicular to y=4%2Ax%2B8 and goes through (2,-7) is y=%28-1%2F4%29%2Ax-13%2F2


So here are the graphs of the equations y=4%2Ax%2B8 and y=%28-1%2F4%29%2Ax-13%2F2




graph of the given equation y=4%2Ax%2B8 (red) and graph of the line y=%28-1%2F4%29%2Ax-13%2F2(green) that is perpendicular to the given graph and goes through (2,-7)

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
the standard slope-intercept form for an equation of a line
where m is the slope and b the y-intercept is:
y+=+highlight_green%28m%29x+%2B+highlight%28b%29
4x = y - 8 0r y = 4x + 8 , m = 4 Green
***Using point-slope form, y+-+y%5B1%5D+=+highlight_green%28m%29%28x+-+x%5B1%5D%29
P(2,-7), m = -1/4 (negative reciprocal, line perpendicular)
y + 7 = (-1/4)(x - 2)
y + 7 = (-1/4)(x) +1/2
y = (-1/4)x - 13/2 Blue