Question

(a,b) is a point on a line with slope 2/3. Give the coordinates of another point on the line in terms of a and b.

Answer 1

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

slope = {\color{green}{ m}}= \cfrac{rise}{run}= \cfrac{2}{3}\impliedby \cfrac{\textit{up by that much}}{\textit{sideways by that much}}\)

Answer 2

So I just choose whatever points I want and then find another point for the second one that uses the 2/3?

Answer 3

yes, you could use (0,0) since it didn't specify.