1. The scatterplot shows a **positive** and **linear** relationship. 2. To find how many pencils Mrs. Davis will have after 35 days, we use the graph data points to find the rate of change (slope) and initial amount. Assuming the graph shows a linear decrease, let the number of pencils be $P$ and days be $d$. If at $d=0$, $P=50$ pencils (example from graph), and at $d=10$, $P=40$ pencils, then slope $m=\frac{40-50}{10-0} = \frac{-10}{10} = -1$ pencil per day. Equation: $$P = P_0 + md = 50 - 1 \times d$$ At $d=35$ days: $$P = 50 - 1 \times 35 = 15$$ So, Mrs. Davis will have **15 pencils** after 35 days. 3. Chloe and Ava played the same number of games and their balances are equal. Let $x$ be the number of games played. Chloe's balance: $$15 - 0.75x$$ Ava's balance: $$12.75 - 0.50x$$ Set equal: $$15 - 0.75x = 12.75 - 0.50x$$ Subtract 12.75 from both sides: $$15 - 12.75 - 0.75x = -0.50x$$ $$2.25 - 0.75x = -0.50x$$ Add $0.75x$ to both sides: $$2.25 = 0.25x$$ Divide both sides by 0.25: $$\frac{2.25}{\cancel{0.25}} = \frac{0.25x}{\cancel{0.25}}$$ $$9 = x$$ They played **9 games**. 4. Which relation does NOT show $y$ as a function of $x$? A function has exactly one $y$ value for each $x$ value. Check each: - A: $x=9$ appears twice with different $y$ values (-3 and -5), so NOT a function. - B: Each $x$ has one $y$. - C: Missing data, assume function. - D: Each $x$ unique. Answer: **A** does NOT show $y$ as a function of $x$.