Answer
$-\dfrac{b}{a}$
Work Step by Step
If we have the $x$-intercept and $y$-intercept of the line, then we already have two points on the line; therefore, we can plug these points into the formula for slope. The formula for slope is:
$$m = \dfrac{y_{2} - y_{1}}{x_{2} - x_{1}}$$
Let us plug in the points we are given into this formula:
$$m = \dfrac{b - 0}{0 - a} = \dfrac{b}{- a}=-\dfrac{b}{a}$$
