The rate of change is measured by the slope m.
In case of y=3x-6, the slope is the coefficient of x, that is, the slope m is
[tex]m=3[/tex]
Now, in the case of the table, we must find the slope m by choosing two points. The slope formula in this case is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
where we chose:
[tex]\begin{gathered} (x_1,y_1)=(2,9) \\ (x_2,y_2)=(4,16) \end{gathered}[/tex]
Then, by substituting these values into the slope formula, we have
[tex]\begin{gathered} m=\frac{16-9}{4-2} \\ m=\frac{7}{2} \\ m=3.5 \end{gathered}[/tex]
By comparing the slopes, we can see that the function represented in the table has the greatest rate of chance because 3.5>3
