Question

What is the average rate of change for a function with the equation $2x+3y+6=0$?

Answer 1

Determine the average rate of change for a function.

Rewrite the given equation:

$2x+3y=-6$

Compare the given equation with the standard form of a linear equation, $Ax+By=C$:

$\begin{array}{rcl}A& =& 2\\ B& =& 3\\ C& =& -6\end{array}$

It is known that the average rate of the linear equation is $-\left(\frac{A}{B}\right)$. Determine the average rate of the given function:

$-\left(\frac{2}{3}\right)=\frac{-2}{3}$

Thus, the average rate of the given function is $\frac{-2}{3}$.