Question

Which function has a greater rate of change?

Answer 1

Function 1 passes through (0,0) and (1,2) .

So, equation of function 1 is :

`y - 0 = (2-0)/(1-0)(x-0)`

y = 2x

Function 2 is : y = 0.5x + 7

We know coefficient of x in linear equation is the slope.

Also, rate of change is directly proportional to slope.

Therefore, function 1 has a greater rate of change.

Answer 2

Given:

Graph of function 1.

The equation of function 2 is
`y=(1)/(2)x+7`.

To find:

The function which has a greater rate of change.

Explanation:

From the given graph it is clear that, the function 1 passes through two points (0,0) and (1,2). So, slope of function is

`m=(y_2-y_1)/(x_2-x_1)`

`m=(2-0)/(1-0)`

`m=(2)/(1)`

`m=2`

So, rate of change of function 1 is 2.

On comparing the equation
`y=(1)/(2)x+7` with
`y=mx+b`, where m is slope and b is y-intercept, we get

`m=(1)/(2)`

So, rate of change of function 2 is
`(1)/(2)`.

Since,
`2>(1)/(2)`, therefore, function 1 has a greater rate of change.