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

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Answer 1 · 2018-02-06T20:51:43

See a solution process below:

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

$\frac{f (b) - f (a)}{b - a}$ $(f(b) - f(a))/(b - a)$

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

And

$f (4) = y_{b} = (5 \times 4) + 10 = 20 + 10 = 30$ $f(4) = y_b = (5 xx 4) + 10 = 20 + 10 = 30$

$f (0) = y_{a} = (5 \times 0) + 10 = 0 + 10 = 10$ $f(0) = y_a = (5 xx 0) + 10 = 0 + 10 = 10$

Substituting this into the formula gives:

$\frac{f (b) - f (a)}{b - a} = \frac{30 - 10}{4 - 0} = \frac{20}{4} = 5$ $(f(b) - f(a))/(b - a) = (30 - 10)/(4 - 0) = 20/4 = 5$

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

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