SOLUTION: I have two question. write the equation of the line. Through (8,-9), perpendicular to 7x + 9y = -25 question #2 is through (-6,-7) parallel to -2x + 7y=26 Can you please Help?

Algebra ->  Equations -> SOLUTION: I have two question. write the equation of the line. Through (8,-9), perpendicular to 7x + 9y = -25 question #2 is through (-6,-7) parallel to -2x + 7y=26 Can you please Help?      Log On


   

Question 241609: I have two question.
write the equation of the line. Through (8,-9), perpendicular to 7x + 9y = -25
question #2 is through (-6,-7) parallel to -2x + 7y=26
Can you please Help?????
Found 2 solutions by Alan3354, josmiceli:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
write the equation of the line.
Through (8,-9), perpendicular to 7x + 9y = -25
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Find the slope, m, of the line by putting the eqn into slope-intercept form,
y = mx + b
That means solve for y:
7x + 9y = -25
9y = -7x - 25
y = (-7/9)x - 25/9
The slope is -7/9
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The slope of lines perpendicular is the negative inverse, +9/7.
Use y = mx + b again with the point to find b:
-9 = (9/7)*8 + b
b = -9 - 72/7
b = -135/7
--> y = (9/7)x - 135/7 slope-intercept form
or 9x - 7y = 135 Standard form
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question #2 is through (-6,-7) parallel to -2x + 7y=26
Do it the same way.
If you have questions, or to check your work, email me at
gsihoutx@aol.com

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The rule is: if you have a line with slope = m, then
ANY line perpendicular to it will have slope = -%281%2Fm%29
So, first you have to find the slope of your line.
Get it into the form y+=+mx+%2B+b where m = slope
7x+%2B+9y+=+-25
9y+=+-7x+-+25
y+=+-%287%2F9%29%2Ax+-+25%2F9
You can see that m+=+-%287%2F9%29
Now you have to find -%281%2Fm%29
Divide both sides by m
1+=+-%287%2F9%29%2A%281%2Fm%29
Divide both sides by 7%2F9
1%2F%287%2F9%29+=+-%281%2Fm%29
9%2F7+=+-%281%2Fm%29
So, ANY line perpendicular to the given line will have this slope
The line you're looking for passes through (8,-9)
The formula is
%28y+-+y%5B1%5D%29%2F%28x+-x%5B1%5D%29+=+m where( x%5B1%5D, y%5B1%5D) is the given point
%28y+-+%28-9%29%29%2F%28x+-+8%29+=+9%2F7
Multiply both sides by x-8
y+%2B+9+=+%289%2F7%29%2A%28x-8%29
y+%2B+9+=+%289%2F7%29%2Ax+-+72%2F7
y+=+%289%2F7%29%2Ax+-+63%2F7+-+72%2F7
y+=+%289%2F7%29%2Ax+-+135%2F7 answer
Or, if you like,
9x+-+7y+-+135+=+0
I'll plot both lines