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Which function has a greater rate of change?

Which Function Has A Greater Rate Of Change class=

Sagot :

Given:

Graph of function 1.

The equation of function 2 is [tex]y=\dfrac{1}{2}x+7[/tex].

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

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\dfrac{2-0}{1-0}[/tex]

[tex]m=\dfrac{2}{1}[/tex]

[tex]m=2[/tex]

So, rate of change of function 1 is 2.

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

[tex]m=\dfrac{1}{2}[/tex]

So, rate of change of function 2 is [tex]\dfrac{1}{2}[/tex].

Since, [tex]2>\dfrac{1}{2}[/tex], therefore, function 1 has a greater rate of change.

Solution :

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

So, equation of function 1 is :

[tex]y - 0 = \dfrac{2-0}{1-0}(x-0)[/tex]

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.

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