1. **Problem Statement:** We are given the equation for the total cost of notebooks and pencils: $$1.00 n + 0.25 p = 10.00$$ where $n$ is the number of notebooks and $p$ is the number of pencils. 2. **Understanding the equation:** This is a linear equation representing a line on the coordinate plane with $n$ on the x-axis and $p$ on the y-axis. 3. **Rewrite the equation to solve for $p$:** $$1.00 n + 0.25 p = 10.00$$ Subtract $1.00 n$ from both sides: $$\cancel{1.00} n + 0.25 p - \cancel{1.00} n = 10.00 - 1.00 n$$ which simplifies to: $$0.25 p = 10.00 - 1.00 n$$ 4. **Divide both sides by 0.25 to isolate $p$:** $$p = \frac{10.00 - 1.00 n}{0.25}$$ Using cancellation notation: $$p = \frac{10.00 - 1.00 n}{\cancel{0.25}} \times \frac{1}{\cancel{0.25}} = 40 - 4 n$$ 5. **Interpretation:** The equation $p = 40 - 4 n$ means: - When $n=0$, $p=40$ (y-intercept). - The slope is $-4$, meaning for each additional notebook, you can buy 4 fewer pencils to keep the total cost $10.00$. 6. **Regarding points A and C:** - Point A: $(6,6)$ is not on the line because substituting $n=6$, $p=6$ gives total cost $1.00\times6 + 0.25\times6 = 6 + 1.5 = 7.5$, which is less than 10. - Point C: $(2,2)$ is also not on the line because $1.00\times2 + 0.25\times2 = 2 + 0.5 = 2.5$, less than 10. Only points on the line satisfy the equation exactly. **Final answer:** The line equation is $$p = 40 - 4 n$$ and points A and C do not lie on this line because their total cost is less than 10.