SOLUTION: Write an equation in point-slope form of the line through the point (2, 3) perpendicular to the line with equation y=7/5x+4

Algebra ->  Linear-equations -> SOLUTION: Write an equation in point-slope form of the line through the point (2, 3) perpendicular to the line with equation y=7/5x+4      Log On


   

Question 1128116: Write an equation in point-slope form of the line through the point (2, 3) perpendicular to the line with equation y=7/5x+4
Found 3 solutions by Boreal, josmiceli, josgarithmetic:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
the slope of the line is 7/5, so the slope of the line perpendicular to it is -5/7, the negative reciprocal.
point slope formula y-y1=m(x-x1), m slope, (x1, y1) point
y-3=(-5/7)(x-2)
y-3=-(5/7)x+10/7
y=(-5/7)x+31/7
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C%287%2F5%29x%2B4%2C%28-5%2F7%29x%2B31%2F7%29

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Any line perpendicular to the given line has
slope = +-1%2Fm+=+-5%2F7+
Use the general point-slope formula
+%28+y+-+3+%29+%2F+%28+x+-+2+%29+=+-5%2F7+
Multiply both sides by +7%2A%28+x+-+2+%29+
+7%2A%28+y+-+3+%29+=+-5%2A%28+x+-+2+%29+
+y+-+3+=+%28-5%2F7%29%2A%28+x+-+2+%29+
check:
+7y+-+21+=+-5x+%2B+10+
+7y+=+-5x+%2B+31+
+y+=+%28-5%2F7%29%2Ax+%2B+31%2F7+
( 2,3 )
+3+=+%28-5%2F7%29%2A2+%2B+31%2F7+
+3+=+-10%2F7+%2B+31%2F7+
+3+=+21%2F7+
+3+=+3+
OK

Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
-------------------------------------
Write an equation in point-slope form of the line through the point (2, 3) perpendicular to the line with equation y=7/5x+4
-----------------------------------

recognizing needed slope and plugging-in the values:

y-3=-%285%2F7%29%28x-2%29