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Let $P$ and $Q$ be constants. The graphs of the lines $x + 5y = 7$ and $15x + Py = Q$ are perpendicular and intersect at the point $(-8,3).$ Enter the ordered pair $(P,Q).$

 Jun 28, 2020
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Write x+5y=7 in slope intercept form.

 

x+5y=7

5y=-x+7

y=-x/5+7/5

 

The slope of the perpendicular line, 15x+Py=Q must be 5.

 

15x+Py=Q

Py=-15x+Q

y=-15/Px+Q/P

 

-15/P must equal to 5 so P=-3. We substitute the given point into 15x-3y=Q.

 

15x-3y=Q

15(-8)-3(3)=Q

-120-9=Q

Q=-129

 

(-3, -129)

 
 Jun 28, 2020

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