Question 29

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Jambmaths question: 

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

Option A: 

$\tfrac{7}{8}$

Option B: 

$\tfrac{6}{7}$

Option C: 

$-\tfrac{2}{7}$

Option D: 

$-\tfrac{6}{7}$

Jamb Maths Solution: 

$\begin{align}  & {{l}_{1}}:2y+8x-17=0 \\ & 2y=-8x+17 \\ & y=-\frac{8x}{2}+\frac{17}{2} \\ & y=-4x+\frac{17}{2}\text{    }\!\!\{\!\!\text{ }y=mx+c,\text{ }m=slope\} \\ & {{m}_{1}}=-4 \\ & \text{For two line to parallel }{{m}_{1}}={{m}_{2}} \\ & \text{The slope of }{{m}_{2}}=-4 \\ & \text{Slope of the point }(-1,-p)\text{ and }(-2p,2) \\ & {{m}_{2}}=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}} \\ & \frac{2-(-p)}{-2p-(-1)}=-4 \\ & \frac{2+p}{-2p+1}=-4 \\ & 2+p=-4(-2p+1) \\ & 2+p=8p-4 \\ & 7p=6 \\ & p=\frac{6}{7} \\\end{align}$

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