Question

A line contains the points (4,-3) and (1, -2). Another line graphed in the same coordinate plane contains the points (-2,0) and (-3,-3).
Based on the slope of these lines, are they parallel, perpendicular or neither?

Answer 1

perpendicular

Answer 2

find their slopes to find out first \(\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
&({\color{red}{ 4}}\quad ,&{\color{blue}{ -3}})\quad &({\color{red}{ 1}}\quad ,&{\color{blue}{ -2}})\\
&({\color{red}{ -2}}\quad ,&{\color{blue}{ 0}})\quad &({\color{red}{ -3}}\quad ,&{\color{blue}{ -3}})
\end{array}
\\\quad \\

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}}}\)