SOLUTION: Please help me solve this equation: Equation of line passing through (-7,-9) and perpendicular to 8x-9y+2=0 What I've tried: y=-8/9x+2/9 PL: y=9/8x+b EQUALS -9=9/8(-7)+b ??? H

Algebra ->  Linear-equations -> SOLUTION: Please help me solve this equation: Equation of line passing through (-7,-9) and perpendicular to 8x-9y+2=0 What I've tried: y=-8/9x+2/9 PL: y=9/8x+b EQUALS -9=9/8(-7)+b ??? H      Log On


   

Question 582392: Please help me solve this equation:
Equation of line passing through (-7,-9) and perpendicular to 8x-9y+2=0
What I've tried: y=-8/9x+2/9 PL: y=9/8x+b EQUALS -9=9/8(-7)+b ???
Help please.
Found 2 solutions by josmiceli, KMST:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
In general, if the line is +y+=+m%5B1%5D%2Ax+%2B+b+,
then the line perpendicular to it has a slope
+m%5B2%5D+=+-%28+1%2F%28m%5B1%5D%29+%29+
given:
+8x+-+9y+%2B+2+=+0+
+9y+=+8x+%2B+2+
+y+=+%288%2F9%29%2Ax+%2B+2%2F9+
Any line perpendicular to this one has slope
+m%5B2%5D+=++-%281%2F%288%2F9%29%29+
+m%5B2%5D+=+-%289%2F8%29+
------------------
given that the line passes through (-7,-9 )
Now use the point-slope formula:
+%28+y+-+%28-9%29+%29+%2F+%28+x+-+%28-7%29+%29+=+-%289%2F8%29+
+%28+y+%2B+9+%29+%2F+%28+x+%2B+7+%29+=+-%289%2F8%29+
Multiply both sides by +8%2A%28+x+%2B+7+%29+
+8%2A%28+y+%2B+9+%29+=+-9%2A%28+x+%2B+7+%29+
+8y+%2B+72+=+-9x+-+72+
+9x+%2B+8y+%2B+144+=+0+
Here's a plot of the 2 lines:

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
8x-9y%2B2=0 --> 8x%2B2=9y --> 8x%2F9%2B2%2F9=y or y=%288%2F9%29x%2B2%2F9
The slope of the given line is 8%2F9.
A perpendicular line will have a slope of -9%2F8
Setting up an equation such as -9=-7%28-9%2F8%29%2Bb and solving for b would work.
-9=-7%28-9%2F8%29%2Bb --> -9=63%2F8%2Bb --> b=%28-63%2F8%29-9 --> b=-63%2F8-72%2F8 --> b=-135%2F8
Otherwise, the point slope form of the equation is
y-%28-9%29%29=%28-9%2F8%29%28x-%28-7%29%29 --> y%2B9=%28-9%2F8%29%28x%2B7%29 --> y%2B9=%28-9%2F8%29x%2B7%28-9%2F8%29 --> y%2B9=%28-9%2F8%29x-63%2F8 --> y=%28-9%2F8%29x-63%2F8-9 --> y=%28-9%2F8%29x-63%2F8-72%2F8 --> y=%28-9%2F8%29x-135%2F8
graph%28300%2C300%2C-16%2C4%2C-16%2C4%2C8x%2F9%2B2%2F9%2C-9x%2F8-135%2F8%29