SOLUTION: find the equation of the line that is perpendicular to the line that passes through the points (5,-2) and (-3,14) and passes through (7,9)

Algebra ->  Test -> SOLUTION: find the equation of the line that is perpendicular to the line that passes through the points (5,-2) and (-3,14) and passes through (7,9)      Log On


   

Question 664966: find the equation of the line that is perpendicular to the line that passes through the points (5,-2) and (-3,14) and passes through (7,9)
Answer by ReadingBoosters(3246) About Me  (Show Source):
You can put this solution on YOUR website!
Perpendicular lines have a negative reciprocal slope.
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First, find the slope of the line through (5, -2) and (-3, 14)
slope = %2814-%28-2%29%29%2F%28-3+-+5%29+=+%2816%2F-8%29+=+-2
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The negative reciprocal slope for the perpendicular line is 1%2F2
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Using the slope and the coordinates (7, 9), solve for y-intercept following
y=mx+b
9 = 1%2F27 + b
b = 9 - 1%2F27 = 18%2F2 - 7%2F2 = 11%2F2
The linear equation for the perpendicular line that passes through (7, 9) is:
highlight%28y+=+%281%2F2%29x+%2B+%2811%2F2%29%29
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Red line --> line through (5, -2) and (-3, 14)
Green line --> perpendicular line through (7, 9)
graph%28300%2C200%2C-10%2C10%2C-10%2C10%2C-2x%2B8%2C+%281%2F2%29x%2B%2811%2F2%29%29
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