Linear functions are like straight lines on a graph, and they show up everywhere in real life! They help us describe situations where things change at a constant rate. For example, the cost of a taxi ride (with a starting fee plus a per-mile charge) or the distance you travel at a steady speed can both be modeled using linear functions. Understanding them lets us make predictions and solve problems.
Match the term with its definition:
| Term | Definition |
|---|---|
| 1. Slope | A. The starting value of a linear function |
| 2. Y-intercept | B. A function whose graph is a straight line |
| 3. Linear Function | C. The point where the line crosses the y-axis |
| 4. Rate of Change | D. The measure of how much a function changes for each unit increase in the input |
| 5. Initial Value | E. Another name for the slope |
A linear function can be written in the form $y = mx + b$, where $m$ represents the _______ and $b$ represents the _______. In a real-world context, $m$ often tells us the _______, and $b$ is the _______.
Describe a real-world situation that can be modeled with a linear function. Explain what the slope and y-intercept would represent in that situation.
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