coordinate geometry

Question

Find the value of p if the line that passes through (-1,-p) and (-2p,2) is parallel to the line 8x+2y-17=0

Answer 1

A parallel line to the line 8x+2y-17=0 is a line that has the same slope.

 

Rearranging terms 2y=-8x+17, y=(-8/2)x+(17/2), y=-4x+(17/2), and therefore the slope is -4

 

using the slope form equation (y2-y1)(/x2-x1) = -4, substituting (2+p)/(-2p+1)=-4,

 

expanding 2+p = 8p-4 rearranging 8p-p = 2+4, 7p = 6, p=(6/7)