1. **Stating the problem:** We have two types of golf memberships with different cost structures. We want to find a linear function for the greenfeemedlemskap cost and determine when the fullständigt medlemskap becomes cheaper. 2. **Define variables and functions:** Let $x$ be the number of times played in a year. - Greenfeemedlemskap cost function: $f(x) = kx + m$ - Fullständigt medlemskap cost is fixed at 4275. 3. **Set up the greenfeemedlemskap function:** From the table, the annual fee is 2000 and the cost per play is 150. So, $$f(x) = 150x + 2000$$ 4. **Find when fullständigt medlemskap is cheaper:** We want to find $x$ such that $$4275 < 150x + 2000$$ 5. **Solve the inequality:** $$4275 < 150x + 2000$$ Subtract 2000 from both sides: $$4275 - 2000 < 150x$$ $$2275 < 150x$$ Divide both sides by 150: $$\frac{2275}{150} < x$$ Show cancellation: $$\frac{\cancel{2275}}{\cancel{150}} < x$$ Calculate: $$15.166\ldots < x$$ 6. **Interpretation:** You need to play more than approximately 15.17 times for the fullständigt medlemskap to be cheaper. **Final answers:** - a) $f(x) = 150x + 2000$ - b) $x > 15.17$ times