Example4.5.13

Plot \(y=-\frac{2}{3}x+10\) and \(y=3x+5\text{.}\) These plots follow the approach form the previous example, but there is no context to the equation.

(a)With no context, we only need to make sure that the \(y\)-intercept will be visible, and that any “run” and “rise” amounts we wish to use will not make triangles that are too big or too small.
(b)The slope is \(-\frac{2}{3}=\frac{-2}{3}=\frac{2}{-3}\text{.}\) So we can try using a “run” of \(3\) and a “rise” of \(-2\) or a “run” of \(-3\) and a “rise” of \(2\text{.}\)
(c)Arrowheads and labels are encouraged.
Figure4.5.14Graphing \(y=-\frac{2}{3}x+10\)
(a)With no context, we only need to make sure that the \(y\)-intercept will be visible, and that any “run” and “rise” amounts we wish to use will not make triangles that are too big or too small.
(b)The slope is a whole number \(3\text{.}\) Every \(1\) unit forward causes a change of positive \(3\) in the \(y\)-values.
(c)Arrowheads and labels are encouraged.
Figure4.5.15Graphing \(y=3x+5\)
in-context