Question

What is the rate of change for the formula `y = 5x + 10` over the interval `[0, 4]`?

Answer 1

See a solution process below:

Explanation:

The formal for the average rate of change over a closed interval `[a, b]` is:

`(f(b) - f(a))/(b - a)`

So for this problem the interval is: `[0, 4]`

And

`f(4) = y_b = (5 xx 4) + 10 = 20 + 10 = 30`

`f(0) = y_a = (5 xx 0) + 10 = 0 + 10 = 10`

Substituting this into the formula gives:

`(f(b) - f(a))/(b - a) = (30 - 10)/(4 - 0) = 20/4 = 5`

For a linear equation the rate of change over any interval is the slope which for this equation is also `5`.