Question

The graph below plots a function f(x): graph of line segment going through ordered pairs 0, 100 and 3, 220 If x represents time, the average rate of change of the function f(x) in the first three seconds is ___.

Answer 1

Rate of change is like slope. Use the slope formula:
m = (y2 - y1)/(x2 - x1)
m =(220 - 100)/(3 - 0)
m = 120/3
m = 40

Answer 2

Average rate of change of a line is its slope.

To find slope we can use the formula:

`m=\frac{y_(2)-y_(1)}{x_(2)-x{1}}`

Where,

• m is the slope
• 
  `(x_(1), y_(1))` is the first point
• 
  `(x_(2), y_(2))` is the second point

For our problem,

• Point 1 (
  `(x_(1), y_(1))`) is (0,100)
• Point 2 (
  `(x_(2), y_(2))`) is (3,220)

Now, let's find slope.

`m=(220-100)/(3-0) =(120)/(3) =40`

So, the average rate of change of the function f(x) int he first three seconds is 40.

ANSWER: 40