Let P and Q be constants. The graphs of the lines x + 5y = 23 and 16x + Py = Q are perpendicular and intersect at the point (8,3). Enter the ordered pair (P,Q).

Guest Apr 14, 2022

#1

#18**+1 **

Slope of first line = - 1/5 perpindicular is = 5

16x + py = q slope = -16/p = 5 p = - 16/5

16 x - 16/5 p = q sub in the point (8,3) to find the value of Q = 118.4

Guest Apr 14, 2022

#19**+1 **

We can write the first line as

y = (-1/5)x + 23/5 Note that the slope = -1/5

If the second ine is perpendicular to this one, then it will have a slope of 5

So we have that

16x + Py = Q

Py = -16x + Q

y = (-16/P ) + Q/P

This means that -16/P = 5 so P = -16/5

And since (8,3) is on this line then

16 (8) + (-16/5)(3) =Q

128 - 48/5 = Q

592/5 = Q

So (P, Q) = (-16/5, 592/5)

CPhill Apr 14, 2022

#21**+1 **

Because the lines are perpendicular, the other line has a slope of \(5\).

This means that the equation is \(y = 5x + b\)

Plugging in the point (8, 3), we get: \(3= 40+b\), meaning \(b = -37\)

Now, we have to convert \(y = 5x - 37\) into standard form.

Subtracting \(5x\) from both sides, we get \(-5x + y = -37\)

Multiplying the equation by \(-{16 \over 5}\) , we get: \(16x-3.2y=118.4\)

From here, we can find the pair to be \(\color{brown}\boxed{(-3.2, 118.4)}\)

BuilderBoi Apr 14, 2022

#25**+1 **

No, our answers are the same... I just did mine in decimal, and Chris did his in fraction form.

BuilderBoi
Apr 14, 2022