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Two linear functions are shown below. Which function has the greater rate of change? Function A: 4 8 12. y 1 2 3 4 Function B: y= 0.75x - 2​

Two linear functions are shown below Which function has the greater rate of change Function A 4 8 12 y 1 2 3 4 Function B y 075x 2 class=

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akposevictor

Answer:

Function B

Step-by-step explanation:

✍️Rate of change for Function A:

Using any two pairs from the table of values given, say, (0, 1) and (4, 2):

Rate of change = [tex] \frac{y_2 - y_1}{x_2 -x_1} = \frac{2 - 1}{4 - 0} = \frac{1}{4} [/tex]

Rate of change for function A = ¼ = 0.25

✍️Rate of change for Function B:

Equation for Function B is given in the slope-intercept format, y = mx + b.

m = slope = rate of change.

Therefore, the function, y = 0.75x - 2 has a rate of change of 0.75.

Rate of change of Function B = 0.75.

✅0.75 if greater than 0.25, therefore, Function B has the greater rate of change.

boffeemadrid

The function which has a greater rate of change or slope is required.

Function B has a greater rate of change.

Rate of change is given by

[tex]m=\dfrac{\Delta y}{\Delta x}[/tex]

The ordered pairs for the first function are

[tex](0,1),(4,2),(8,3),(12,4)[/tex]

Slope

[tex]m=\dfrac{2-1}{4-0}=\dfrac{1}{4}=0.25[/tex]

Since, it is a linear equation the slope will be equal for all ordered pairs.

The point slope form of a line is

[tex]y=mx+c[/tex]

where

m = Slope or rate of change

c = y intercept

Here, the equation is

[tex]y=0.75x-2[/tex]

The slope is 0.75.

Function B has a greater rate of change.

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