Q. 11 - Precalculus Enhanced with Graphing Utilities

Question

True or False If the average rate of change of a linear function is $\frac{2}{3}$, then if $y$ increases by $3$, $x$ will increase by $2$. 

Step-by-Step Solution

Answer

The given statement is false.

Step 1 Given information

If the average rate of change of a linear function is$\frac{2}{3}$ , then if $y$ increases by$3$ ,  $x$will increase by $2$ . 

Step 2 Solution

Linear functions have a constant average rate of change. That is, the average rate of change of a linear function $y=mx+b$is

$\frac{∆y}{∆x}=m.$

Here, $∆x=2$ and $∆y=3,$then $m=\frac{∆y}{∆x}=\frac{3}{2}.$

Step 3 Final answer

Hence, the given statement is false.