Answer
$\text{m=}\frac{-b}{a}$ ; falls
Work Step by Step
The slope of a line can be defined as the ratio of the vertical change to the horizontal change when moving from one fixed point to another along a line.
The general notation for the slope of a line is, $\left( m \right)$.
$\text{m= }\frac{\text{change in vertical}}{\text{change in horizontal}}$
Let $\left( {{x}_{1}},{{y}_{1}} \right)$ represents point $\left( -a,0 \right)$ and $\left( {{x}_{2}},{{y}_{2}} \right)$ represents point $\left( 0,-b \right)$
Then,
$\begin{align}
& \text{m= }\frac{\text{change in vertical}}{\text{change in horizontal}} \\
& =\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}} \\
& =\frac{\left( -b \right)-0}{0-\left( -a \right)} \\
& =-\frac{b}{a}
\end{align}$
Hence, the slope of the line is $-\frac{b}{a}$
As the slope is negative, therefore the line passing through the provided point is falling.
