Key Concepts:
- To translate word problems into equations, identify the variables and the relation between them.
- The slope represents the rate of change (like speed or cost per item).
- The y-intercept often represents a starting value (e.g., initial deposit in a bank account).
- Linear functions model real-world relationships such as pricing, uniform motion, and temperature changes, which are often related to linear graphs.
Skills Covered:
- Writing a linear equation and solving for unknowns from a word problem.
- Interpreting the meaning of slope and intercept in real-world contexts.
- Interpreting relationships in word problems through graphs.
Example Problems:
- A store sells two types of fruit. Apples cost $2 each, and oranges cost $3 each. If a customer spends $18 and buys 7 fruits, how many of each did they buy?
- A runner jogs for x miles at 5 mph and then runs for y miles at 8 mph, covering a total of 13 miles. Write an equation for the situation.
- A gym charges $30 per month plus a $50 sign-up fee. Calculate the total cost after x months.
- The temperature T in Fahrenheit is given by (T = 1.8K - 459.67), where (K) is Kelvin. How much does the Fahrenheit temperature increase if Kelvin increases by 50?