Question

bria starts with $8 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 bria babysits and the dollars in her account a linear relationship? no, it is not a linear relationship. yes, it is 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 $b$ is the initial value.

Step2: Identify given values

Initial amount $b = 8$, hourly rate $m = 12$. The equation is $y = 12x + 8$.

Step3: Verify constant rate of change

Check the plotted points:

• At $x=0$, $y=8$
• At $x=1$, $y=12(1)+8=20$
• At $x=2$, $y=12(2)+8=32$
• At $x=3$, $y=12(3)+8=44$

The change in $y$ per 1 unit $x$ is always 12, constant.

Answer:

Yes, it is a linear relationship.