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

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.

$m=\frac{220-100}{3-0} =\frac{120}{3} =40$

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

ANSWER: 40

Answer 2

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