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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).

 Feb 22, 2020
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We can solve for y in the equation x + 5y = 7 to get y = -1/5*x + 7/5, so the slope of the line is -1/5.

 

Then the perpendicular line will have slope -5.  We want the perpendicular line to go through (-8,3), so by point-slope form, the equation of the line is y - 3 = -5(x + 8).  Expanding, we get y = -5x - 37, so 5x + y = -37.

 

We want the coefficient of x to be 15, so we multiply by 3: 15x + 3y = -111.  Therefore, (A,B) = (3,-111).

 Feb 22, 2020

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