Question

Why is the slope of the line that passes through (a,b) and (-a,b)

Answer 1

May I assume that you know the general slope formula? If so, please type it here. Then we'll move on to solving the problem you've posted.

Answer 2

\(\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
&({\color{red}{ a}}\quad ,&{\color{blue}{ b}})\quad &({\color{red}{ -a}}\quad ,&{\color{blue}{ b}})
\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}}}\)

Answer 3

Thanks, JDoe!

@ktodd7315 : You are given the two points (a,b) and (-a,b). Experiment. See whether you can take the coordinates of these two points, substitute them into the slope formula provided by JDoe, and thus find the slope of the line through (a,b) and (-a,b).