Does it make sense to multiply slopes?

Question

Multiplying fractions is a regular occurance. If those fractions are considered slopes, does it make any sense?

For example, if these fractions are slopes,$\frac{9}{8} \times \frac{49}{48},$ does the product have meaning in terms of slope?

Answer 1

Sure. Let $f(x)=ax+b, g(x)=cx+d$. Then the slope of $f(g(x))$ is $ac$.