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 [tex]\frac{-1}{2}[/tex]
We have to find the value of p
Slope of a line that passing through [tex]\left(x_{1}, y_{1}\right) \text { and }\left(x_{2}, y_{2}\right)[/tex] is given as:
[tex]\mathrm{m}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]\text { Here, in our problem, } x_{1}=3, y_{1}=-1 \text { and } x_{2}=p, y_{2}=2[/tex]
[tex]\text { slope } m=\frac{2-(-1)}{p-3}=\frac{2+1}{p-3}=\frac{3}{p-3}[/tex]
And, according to given information, slope value is given
[tex]\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}[/tex]
Hence, the value of p is [tex]-3[/tex]
