Question

Determine the value of r so that the line through (-2, 5) and (6, r ) has a slope of -3/2.

Answer 1

\(\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({\color{red}{ -2}}\quad ,&{\color{blue}{ 5}})\quad
% (c,d)
&({\color{red}{ 6}}\quad ,&{\color{blue}{ r}})
\end{array}
\\\quad \\
% slope = m
slope = {\color{green}{ m}}= \cfrac{rise}{run} \implies
\cfrac{{\color{blue}{ y_2}}-{\color{blue}{ y_1}}}{{\color{red}{ x_2}}-{\color{red}{ x_1}}}\implies
\cfrac{{\color{blue}{ r}}-{\color{blue}{ 5}}}{{\color{red}{ 6}}-{\color{red}{ (-2)}}}=-\cfrac{3}{2}\)

solve for "r"