Answer:
B. -1.5x − 3.5y = -31.5
Step-by-step explanation:
You forgot to provide the reference image which is essential to answer the question, but I managed to find it... and attach it to my answer.
In the given equation for AB, if we place the y term on the left and x term on the right, we see the slope of that line is 7/3 (y = (7x - 21.5)/3 ==> 7/3x).
We see on the image that the line PQ is perpendicular to AB. That means that its slope is -3/7.
If we quickly check the slopes of each of the possible answers...
A. -3x + 4y = 3 ----> 4y = 3x - 3 ==> y = (3x-3)/4 => slope = 3/4
Not what we're looking for.
B. -1.5x - 3.5y = -31.5 ==> 3.5y = -1.5x + 31 ===> y = (-1.5x +31)/3.5
that gives us a slope of -1.5/3.5... We can simplify it... -3(0.5)/7(0.5) = -3/7
Exactly as predicted.
Since we have the point P (7,6), we can enter it in the equation to verify:
-1.5x - 3.5y = -31.5
-1.5 (7) - 3.5 (6) = -10.5 - 21 = -31.5 --- Verified
C. 2x + y = 20 ==> y = 20 - 2x ===> slope is -2, not what we want.
D. -2.25x + y = -9.75 ==> y = 2.25x - 9.75 ==> slop is 2.25 cannot be it.
