Real-World Linear Problems

A phone plan charges $30/month plus $0.10 per text. Your bill is $42. How many texts did you send? Set up: 30 + 0.10t = 42. Subtract 30: 0.10t = 12. Divide by 0.10: t = 120 texts. Translating words into equations is the hardest part — the algebra is mechanical.

Linear equations model any situation where something grows at a constant rate. Miles driven, money saved weekly, temperature changing hourly — if the rate is steady, the equation is linear. Recognizing this pattern lets you set up and solve the equation before reaching for a calculator.