What is the rate of change of the following equation? y = ( - 5)/(2) x - 5

Question

What is the rate of change of the following equation?
`y = ( - 5)/(2) x - 5`

Answer 1

the given equation is

`y=-(5)/(2)x-5`

we will solve further

`2y=-5x-10`

then we will differentiate the equation with respect to x

`\begin{gathered} 2(dy)/(dx)=-5-0 \\ (dy)/(dx)=-(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.