Question

Let $A$ and $B$ be constants such that the graphs of the lines $x + 5y = 7$ and $15x + Ay = B$ are perpendicular and intersect at $(-8,3).$ Enter the ordered pair $(A,B).$

Answer 1

Answer:

(A, B) = (-3, -129).

Step-by-step explanation:

First convert the first equation to slop-intercept form:

x + 5y = 7

5y = -x + 7

y = -0.2x + 1.4

The slope is -0.2 so the slope of the line perpendicular to this line has slope

-1/ -0.2 = 5.

Now, converting the second equation to slope-intercept form:

15x + Ay = B

Ay = -15x + B

y =  (-15/A)x + B/A

So the slope -15/A = 5 so A = -3.

So y =  5x +  B/-3

Substituting the point (-8, 3)

3 = 5(-8) + B/-3

B/-3 =  43

B = - 129.