Question

A line with a slope id -1/2 passes through the points (3,-1) and (p,2). what is the value of p

Answer 1

The value of p is -3 for the line that passes through (3, -1) and (p, 2)

Solution:

Given, two points are (3, -1) and (p, 2) and slope is $\frac{-1}{2}$

We have to find the value of p

Slope of a line that passing through $\left(x_{1}, y_{1}\right) \text { and }\left(x_{2}, y_{2}\right)$ is given as:

$\mathrm{m}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$\text { Here, in our problem, } x_{1}=3, y_{1}=-1 \text { and } x_{2}=p, y_{2}=2$

$\text { slope } m=\frac{2-(-1)}{p-3}=\frac{2+1}{p-3}=\frac{3}{p-3}$

And, according to given information, slope value is given

$\begin{array}{l}{\frac{3}{p-3}=-\frac{1}{2}} \\\\ {-1(p-3)=3 \times 2} \\\\ {-p+3=6} \\\\ {p=3-6} \\\\ {p=-3}\end{array}$

Hence, the value of p is $-3$