Question

Determine whether the lines through the given pairs of points are parallel. A (2, - 3), B (- 2, - 11) and C (1, 2), D (- 1, 6)

Answer 1

\(\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
A&({\color{red}{ 2}}\quad ,&{\color{blue}{ -3}})\quad B&({\color{red}{ -2}}\quad ,&{\color{blue}{ -11}})
\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}}}\\
----------------------------------\\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
C&({\color{red}{ 1}}\quad ,&{\color{blue}{ 2}})\quad D&({\color{red}{ -1}}\quad ,&{\color{blue}{ 6}})
\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}}}\)

if their slopes are EQUAL, then they're parallel, if not, then they're not