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

Answer Details

Line:  2y+8x-17=0 

recall y = mx + c

2y = -8x + 17

y = -4x  + 172 $\frac{17}{2}$

Slope m1 ${}_1$ = 4

parallel lines: m1 ${}_1$. m2 ${}_2$ = -4

where Slope ( -4) = y2−y1x2−x1 $\frac{y_2-y_1}{x_2-x_1}$ at points (-1, -p) and (-2,2)

-4( x2−x1 $x_2-x_1$ ) = y2−y1 $y_2-y_1$ 

-4 ( -2 - -1) = 2 - -p

p = 4 - 2 = 2