Question

Which linear function has the greatest initial value. Which has the greatest rate of change

Answer 1

A. Function C

B. Function B

Explanation:

We have that the equation in its slope and y-intercept form is the following

`\begin{gathered} y=mx+b \\ m\text{ is the slope and b is the y-intercept} \end{gathered}`

Where the slope can be calculated as follows:

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

We must calculate the equation for each function.

Function A:

`\begin{gathered} m=(15-0)/(6-0)=(15)/(6)=(5)/(2)=2.5 \\ b=0 \\ y=2.5x \end{gathered}`

Function B:

`\begin{gathered} y=3x-1 \\ m=3 \\ b=-1 \end{gathered}`

Function C:

`\begin{gathered} m=(4-2)/(6-0)=(2)/(6)=(1)/(3)=0.33 \\ b=2 \\ y=0.33x+2 \end{gathered}`

The linear function has the greatest initial value is the function C, b = 2

The linear function has the greatest rate of change is the function B, m = 3