To find the average rate of change of the function $y = 2x + 3$ on the interval $[1, 3]$, we use the formula:

$\text{Average rate of change} = \frac{f(b) - f(a)}{b - a}$

where:

• $f(x) = 2x + 3$
• $a = 1$ and $b = 3$

Now, calculate $f(3)$ and $f(1)$:

$f(3) = 2(3) + 3 = 6 + 3 = 9$ $f(1) = 2(1) + 3 = 2 + 3 = 5$

Substitute these values into the formula:

$\text{Average rate of change} = \frac{9 - 5}{3 - 1} = \frac{4}{2} = 2$

So, the average rate of change is $2$.

Would you like further details or have any questions?

Here are some related questions to explore:

1. What is the interpretation of the average rate of change in this context?
2. How does the average rate of change relate to the slope of a line?
3. How would the average rate of change change if the interval was $[2, 5]$?
4. What would the average rate of change be for a non-linear function like $y = x^2$?
5. How is the concept of average rate of change used in calculus?

Tip: The average rate of change of a linear function is constant and equal to the slope of the line.