Rate of Change

A line has the rule $y=5x$. Find the average rate of change from $x=1$ to $x=3$.

• 1Find $y$ at each point: $y$($1$) = $5$, $y$($3$) = $15$
• 2Change in $y=15-5=10$. Change in $x=3-1=2$
• 3Average rate of change = $10÷2=5$

Answer: $5$ (the same as the gradient of the line, as expected)

f($x$) = $x^2$. Find the average rate of change from $x=1$ to $x=3$.

• 1Find f at each point: f($1$) = $1^2=1$, f($3$) = $3^2=9$
• 2Change in $y=9-1=8$. Change in $x=3-1=2$
• 3Average rate of change = $8÷2=4$

Answer: $4$