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

1 Answer
Feb 6, 2018

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#.