To find the horizontal intercept of the graph, we set $y = 0$ because the horizontal intercept occurs where the graph crosses the $x$-axis.

The equation of the line is:

$y = 18 - 3x$

Step 1: Set $y = 0$

$0 = 18 - 3x$

Step 2: Solve for $x$

$3x = 18 \quad \Rightarrow \quad x = \frac{18}{3} = 6$

Final Answer:

The horizontal intercept is at $x = 6$ weeks.

This means Juliana will finish paying back the debt after 6 weeks.

Would you like me to explain this in more detail or go further? Here are 5 follow-up questions to expand on this concept:

1. What does the slope of the line represent in this problem?
2. How do we calculate the vertical intercept, and what does it represent in this scenario?
3. What is the significance of the negative slope in the equation $y = 18 - 3x$?
4. Can you identify other points on the graph that make sense for this problem?
5. How would the graph change if Juliana paid back more money each week?

Tip: The horizontal intercept is where the dependent variable (y) equals 0. For linear equations, this is found by solving for $x$.