Question

What is the rate of change of the following equation? $y = \frac{ - 5}{2} x - 5$

Answer 1

the given equation is

$y=-\frac{5}{2}x-5$

we will solve further

$2y=-5x-10$

then we will differentiate the equation with respect to x

$\begin{gathered} 2\frac{dy}{dx}=-5-0 \\ \frac{dy}{dx}=-\frac{5}{2} \end{gathered}$

so the rate of change is -5/2.

or we can compare the given equation with the standard equation

$y=mx+c$

here, m represent the rate of change,

so the rate of change is -5/2.