Question

If the slope of the line joining the points $(3,-9)$ and $(p,2p+3)$ is $-5/7$ then find the value of $p$.

• A. $\frac{23}{4}$
• B. $\frac{99}{4}$
• C. $\frac{-69}{19}$
• D. $\frac{-99}{4}$

Answer 1

The correct option is C $\frac{-69}{19}$

Let's assume the slope joining the points $(3,-9)$ and $(p,2p+3)$ is $m$

$\Rightarrow m=\frac{2p+3-(-9)}{p-3}=\frac{2p+12}{p-3}$

From the given data we know that slope $m=\frac{-5}{7}$

$\Rightarrow \frac{2p+12}{p-3}=-\frac{5}{7}$

$\Rightarrow 14p+84=-5p+15$

$\Rightarrow p=-\frac{69}{19}$