1. **State the problem:** We are given two payment options for hockey players based on goals scored. We need to find missing values, calculate payments, draw graphs, and analyze the payment options. 2. **Formulas:** - Option A payment: $$\text{Payment}_A = 4600 + 250 \times \text{goals}$$ - Option B payment: $$\text{Payment}_B = 4000 + 400 \times \text{goals}$$ 3. **Calculate missing value P (Option A at 4 goals):** $$P = 4600 + 250 \times 4 = 4600 + 1000 = 5600$$ 4. **Calculate missing value Q (Option B at 6 goals):** $$Q = 4000 + 400 \times 6 = 4000 + 2400 = 6400$$ 5. **Option B payment if 0 goals scored:** $$4000 + 400 \times 0 = 4000$$ 6. **Draw line graph for Option A:** - Plot points using formula for goals 0 to 8. - Example points: (0,4600), (2,5100), (4,5600), (7,6350), (8,6600). 7. **Find goals for R5350 in Option A:** Solve $$4600 + 250x = 5350$$ $$250x = 750$$ $$x = 3$$ So, 3 goals needed. 8. **Compare payments at 5 goals:** - Option A: $$4600 + 250 \times 5 = 4600 + 1250 = 5850$$ - Option B: $$4000 + 400 \times 5 = 4000 + 2000 = 6000$$ Option B pays more. 9. **Find goals where payments are equal:** Solve $$4600 + 250x = 4000 + 400x$$ $$600 = 150x$$ $$x = 4$$ At 4 goals, payments are equal at $$5600$$. 10. **Name of intersection point:** This point is called the **point of intersection** or **equilibrium point** where both payment options yield the same amount. **Final answers:** - P = 5600 - Q = 6400 - Option B payment at 0 goals = 4000 - Goals for R5350 in Option A = 3 - At 5 goals, Option B pays more - Equal payment at 4 goals = 5600 - Intersection point is the equilibrium point