The value of "r" is -3 so the line passes through (r,-2) and (-7,-1) has a slope of m = -1/4
Given that line passes through (r, -2) and (-7, -1) has a slope of [tex]m = \frac{-1}{4}[/tex]
To find: value of r
The slope of line passing through two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is given as:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Here given that slope [tex]m = \frac{-1}{4}[/tex]
[tex]\text {Also } x_{1}=r ; y_{1}=-2 ; x_{2}=-7 ; y_{2}=-1[/tex]
Substituting the values in above formula, we get
[tex]\begin{array}{l}{m=\frac{-1-(-2)}{-7-r}} \\\\ {\frac{-1}{4}=\frac{-1+2}{-7-r}}\end{array}[/tex]
[tex]\begin{array}{l}{\frac{-1}{4}=\frac{1}{-7-r}} \\\\ {7+r=4} \\\\ {r=-3}\end{array}[/tex]
Thus the value of "r" is -3
