Question

carla starts with -$4 in her account. she earns $12 per hour babysitting and deposits the earnings into her account. is the relationship between the number of hours that carla babysits and the dollars in her account a linear relationship? yes, it is a linear relationship. no, it is not a linear relationship.

Explanation:

Step1: Define linear relationship rule

A linear relationship follows the form $y = mx + b$, where $m$ (rate of change) is constant, and plots as a straight line.

Step2: Identify given values

Initial amount (b) = $-4$, hourly rate (m) = $12$. The equation is $d = 12x - 4$.

Step3: Verify plotted points

• For $x=0$: $d = 12(0) - 4 = -4$ (matches the point)
• For $x=1$: $d = 12(1) - 4 = 8$ (matches the point)
• For $x=2$: $d = 12(2) - 4 = 20$ (matches the point)
• For $x=3$: $d = 12(3) - 4 = 32$ (matches the point)

All points lie on the straight line of the linear equation, so the rate of change is constant.

Answer:

Yes, it is a linear relationship.