SOLUTION: Please help me solve this problem: Contains point (-2,-3) and is perpendicular to 5x - 2y = 8. Its a slope-intercept form problem.

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Question 497914: Please help me solve this problem: Contains point (-2,-3) and is perpendicular to 5x - 2y = 8. Its a slope-intercept form problem.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
given:
point (-2,-3)
and is perpendicular to 5x+-+2y+=+8
in a slope-intercept form:
5x+-8=+2y
%285%2F2%29x+-4=+y

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 5%2F2, 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%285%2F2%29 So plug in the given slope to find the perpendicular slope



m%5Bp%5D=%28-1%2F1%29%282%2F5%29 When you divide fractions, you multiply the first fraction (which is really 1%2F1) by the reciprocal of the second



m%5Bp%5D=-2%2F5 Multiply the fractions.


So the perpendicular slope is -2%2F5



So now we know the slope of the unknown line is -2%2F5 (its the negative reciprocal of 5%2F2 from the line y=%285%2F2%29%2Ax-4). Also since the unknown line goes through (-2,-3), 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%2B3=%28-2%2F5%29%2A%28x%2B2%29 Plug in m=-2%2F5, x%5B1%5D=-2, and y%5B1%5D=-3



y%2B3=%28-2%2F5%29%2Ax%2B%282%2F5%29%28-2%29 Distribute -2%2F5



y%2B3=%28-2%2F5%29%2Ax-4%2F5 Multiply



y=%28-2%2F5%29%2Ax-4%2F5-3Subtract -3 from both sides to isolate y

y=%28-2%2F5%29%2Ax-4%2F5-15%2F5 Make into equivalent fractions with equal denominators



y=%28-2%2F5%29%2Ax-19%2F5 Combine the fractions



y=%28-2%2F5%29%2Ax-19%2F5 Reduce any fractions

So the equation of the line that is perpendicular to y=%285%2F2%29%2Ax-4 and goes through (-2,-3) is y=%28-2%2F5%29%2Ax-19%2F5


So here are the graphs of the equations y=%285%2F2%29%2Ax-4 and y=%28-2%2F5%29%2Ax-19%2F5




graph of the given equation y=%285%2F2%29%2Ax-4 (red) and graph of the line y=%28-2%2F5%29%2Ax-19%2F5(green) that is perpendicular to the given graph and goes through (-2,-3)