Respuesta :
ANSWER:
A. Function C
B. Function B
STEP-BY-STEP EXPLANATION:
We have that the equation in its slope and y-intercept form is the following
[tex]\begin{gathered} y=mx+b \\ m\text{ is the slope and b is the y-intercept} \end{gathered}[/tex]Where the slope can be calculated as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]We must calculate the equation for each function.
Function A:
[tex]\begin{gathered} m=\frac{15-0}{6-0}=\frac{15}{6}=\frac{5}{2}=2.5 \\ b=0 \\ y=2.5x \end{gathered}[/tex]Function B:
[tex]\begin{gathered} y=3x-1 \\ m=3 \\ b=-1 \end{gathered}[/tex]Function C:
[tex]\begin{gathered} m=\frac{4-2}{6-0}=\frac{2}{6}=\frac{1}{3}=0.33 \\ b=2 \\ y=0.33x+2 \end{gathered}[/tex]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
