Answer
\[m=-\frac{a}{b},\text{falls}\].
Work Step by Step
Use the formulae \[m=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}\]to find the slope of the line passing through points \[\left( {{x}_{1}},{{y}_{1}} \right)\]and \[\left( {{x}_{2}},{{y}_{2}} \right)\].
Take \[\left( {{x}_{1}},{{y}_{1}} \right)=\left( 0,a \right)\]and \[\left( {{x}_{2}},{{y}_{2}} \right)=\left( b,0 \right)\].
Slope of the line is,
\[m=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}\]
\[\begin{align}
& m=\frac{0-a}{b-0} \\
& =-\frac{a}{b}
\end{align}\]
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 negative so, the line falls from left to right.
