# At what value of p does the graph of the equation y + px = 0 pass through the point

At what value of p does the graph of the equation y + px = 0 pass through the point of intersection of the lines y = -7 / 8x + 17 and y = -3 / 5x-16.

Find the point of intersection of the lines y = -7 / 8x + 17 and y = – 3 / 5x – 16, for this we solve the system of equations:

y = -7 / 8x + 17,

y = – 3 / 5x – 16.

-7 / 8x + 17 = – 3 / 5x – 16,

-7 / 8x + 3 / 5x = -16 – 17,

-11/40 x = 33,

x = -33 * 40/11,

x = -120.

y = -7/8 * 120 + 17 = -88.

The intersection point of the lines has coordinates A (-120; -88).

Because the graph of the function y + px = 0 must pass through point A, then when substituting the coordinates, the correct equality should turn out:

-88 – 120p = 0.

Let us solve for p:

-120r = 88,

p = -88/120,

p = -11/15.

Answer: at p = -11/15, the graph y + px = 0 will pass through the point of intersection of the lines y = -7 / 8x + 17 and y = – 3 / 5x – 16.

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