Answer
\[m=\frac{a}{b},\text{rises}\].
Work Step by Step
Take \[\left( {{x}_{1}},{{y}_{1}} \right)=\left( a-b,c \right)\]and \[\left( {{x}_{2}},{{y}_{2}} \right)=\left( a,a+c \right)\].
Slope of the line is:
\[m=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}\]
\[\begin{align}
& m=\frac{a+c-c}{a-\left( a-b \right)} \\
& =\frac{a}{a-a+b} \\
& =\frac{a}{b}
\end{align}\]
Therefore, the slope of the line is \[\frac{a}{b}\].
There is a vertical change of \[a\] units (\[a\]units down) for each horizontal change of \[b\] units.
The slope is positive.So, the line rises from left to right.
