Let's analyze the image.

The equation of the line is $y = 18 - 3x$, where $y$ represents the amount Juliana owes her brother, and $x$ represents the time in weeks. The horizontal intercept is given as $(6, 0)$.

Explanation:

1. Horizontal Intercept ($6, 0$): This is the point where the amount Juliana owes ($y$) becomes 0.
   • In the context of the problem, this means it will take 6 weeks for Juliana to completely repay the loan.

Representation in the Situation:

The horizontal intercept represents the time required (6 weeks) for Juliana to fully repay the amount borrowed from her brother, assuming she pays back $3 every week.

Would you like additional details on this? Here are some related questions for practice:

1. What is the significance of the vertical intercept in this situation?
2. How much money did Juliana borrow initially?
3. What does the slope $-3$ represent in this context?
4. How much will Juliana owe after 4 weeks?
5. What would happen if she increased her weekly repayment to $4? How would the graph change?

Tip: The slope of the line in repayment problems typically indicates the rate of repayment over time.