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).
This question (or similar) was posted the other day....with the same mistake.... 8,3 is not on the line x - 5y = 7
+128475 Maybe you meant x - 5y = -7 ???
If so....rearrange as
-5y = -x - 7 divide both sides by -5
y = (1/5) + 7/5
The slope of this line = 1/5
A perpendicular line has the slope - 5
Rearrange 15x + Py = Q as
Py = -15x + Q
y = (-15/P)x + Q/P
To have a slope of -5, P must be = 3
So we have
y = -5x + Q/3
And since (8,3) is on this line we have that
3 = -5(8) + Q/3
3 = -40 + Q/3
43 = Q/3 multiply through by 3
129 = Q
So (P,Q) = (3, 129)
