Q:

Caleb made the table below to show the number of hours he works and the amounts he earns over a four-week period. Caleb’s Earnings Hours 12 15 18 21 Earnings (in dollars) 140 170 200 230 Which describes whether the relationship between the earnings and the number of hours represents a direct variation?

Accepted Solution

A:
Answer:The ratios of earnings to hours are not the same each week, so the earnings do not vary directly with the hours.Step-by-step explanation:We know that the data points given by (x,y) are in direct variation if:[tex]\dfrac{y}{x}=k[/tex]  for each (x,y)We are given data as:Caleb’s Earnings Hours(x)        12          15         18         21 Earnings (in dollars)(y)              140        170      200     230 So, we could see the ratio as:[tex]\dfrac{140}{12}=\dfrac{35}{3}[/tex][tex]\dfrac{170}{15}=\dfrac{34}{3}[/tex][tex]\dfrac{200}{18}=\dfrac{100}{9}[/tex][tex]\dfrac{230}{21}[/tex]Hence, we could see that each ratio are not equal.Hence, the relationship between the earnings and the number of hours does not represents a direct variation.