To find the horizontal intercept from the graph and equation $y = 18 - 3x$, we proceed as follows:

Horizontal Intercept Concept

The horizontal intercept occurs where $y = 0$. This is the point where the line crosses the $x$-axis.

Solve for $x$ when $y = 0$:

We use the given equation: $y = 18 - 3x$ Set $y = 0$: $0 = 18 - 3x$ Rearranging for $x$: $3x = 18 \quad \implies \quad x = \frac{18}{3} = 6$

Horizontal Intercept

The horizontal intercept is at: $(6, 0)$

Explanation:

At $x = 6$ weeks, Juliana finishes paying off her debt, so the amount she owes becomes zero.

Would you like more details on intercepts or related graph concepts? Here are some follow-up questions you might explore:

1. What is the vertical intercept of this graph?
2. How do you determine the slope of the line from the equation?
3. What does the slope $-3$ represent in this context?
4. How much did Juliana owe initially?
5. If Juliana paid $4 per week instead, what would the new horizontal intercept be?

Tip: To find any intercept, set the other variable to zero and solve for the remaining variable.