Question

Which function has a greater rate of change?

Answer 1

Given:

Graph of function 1.

The equation of function 2 is $y=\dfrac{1}{2}x+7$.

To find:

The function which has a greater rate of change.

Step-by-step 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

$m=\dfrac{y_2-y_1}{x_2-x_1}$

$m=\dfrac{2-0}{1-0}$

$m=\dfrac{2}{1}$

$m=2$

So, rate of change of function 1 is 2.

On comparing the equation $y=\dfrac{1}{2}x+7$ with $y=mx+b$, where m is slope and b is y-intercept, we get

$m=\dfrac{1}{2}$

So, rate of change of function 2 is $\dfrac{1}{2}$.

Since, $2>\dfrac{1}{2}$, therefore, function 1 has a greater rate of change.

Answer 2

Solution :

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

So, equation of function 1 is :

$y - 0 = \dfrac{2-0}{1-0}(x-0)$

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.