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Sagot :
We need to find the table with the greatest unit rato. Therefore, we need to calculate the rate of change of each table.
The rate of change(slope) can be found using the next formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where m= slope = rate of change.
Option A:
We have the next two points (2,16) and (5,10):
[tex]m=\frac{10-16}{5-2}[/tex][tex]m=-\frac{6}{3}=-2[/tex]Option B:
We have the next two points (2,14) and (6,12):
[tex]m=\frac{12-14}{6-2}=\frac{-2}{4}[/tex]Then:
[tex]m=\frac{-1}{2}[/tex]Option C:
We have the next two points (2,-24) and (5,-15)
[tex]m=\frac{-15-(-24)}{5-2}=\frac{-15+24}{3}=\frac{9}{3}[/tex]Then:
[tex]m=3[/tex]Option D:
We have the next two points (2,-12) and (6,-16)
[tex]m=\frac{-16-(-12)}{6-2}=\frac{-16+12}{4}=\frac{-12}{4}[/tex]Then:
[tex]m=-2[/tex]Option E:
[tex]m=\frac{-17-(-19)}{6-2}=\frac{-17+19}{4}=\frac{2}{4}[/tex]Then:
[tex]m=\frac{1}{2}[/tex]Finally, the greatest rate of change is equal to 3. Therefore, the correct answer is option C
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