The value of r so the line that passes through (-5,2) and (3,r) has a slope of -1/2 is -2
Solution:
Given that line is passing through point (-5, 2) and (3, r)
Slope of the line is [tex]\frac{-1}{2}[/tex]
Need to determine value of r.
Slope of a line passing through point [tex]\left(x_{1}, y_{1}\right) \text { and }\left(x_{2}, y_{2}\right)[/tex] is given by following formula:
[tex]\text { Slope } m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] --- eqn 1
[tex]\text { In our case } x_{1}=-5, y_{1}=2, x_{2}=3, y_{2}=\mathrm{r} \text { and } m=-\frac{1}{2}[/tex]
On substituting the given value in (1) we get
[tex]\begin{array}{l}{-\frac{1}{2}=\frac{r-2}{3-(-5)}} \\\\ {\text { Solving the above expression to get value of } r} \\\\ {=>-\frac{1}{2}=\frac{r-2}{3+5}} \\\\ {=>-8=\frac{r-2}{3+5}} \\\\ {=>-8=2(r-2)} \\\\ {=>-8=2 r-4} \\\\ {=>2 r=-8+4} \\\\ {=>2 r=-4} \\\\ {=>r=\frac{-4}{2}=-2}\end{array}[/tex]
Hence the value of "r" is -2
