๐ Topic Summary
Linear functions are like straight lines on a graph, and they show up everywhere in the real world! They help us understand relationships where things change at a constant rate. For example, the cost of a taxi ride (with a fixed initial fee and a constant per-mile charge) or the distance you travel at a steady speed can both be modeled using linear functions. Learning to solve problems with linear functions will give you tools to make predictions and solve everyday challenges. These worksheets will help you practice translating real-world scenarios into algebraic equations and finding solutions.
๐งฎ Part A: Vocabulary
Match the term with its definition:
| Term |
Definition |
| 1. Slope |
A. The starting value of a linear function |
| 2. Y-intercept |
B. A mathematical sentence stating that two expressions are equal |
| 3. Linear Function |
C. The ratio of the vertical change to the horizontal change |
| 4. Equation |
D. A function whose graph is a straight line |
| 5. Rate of Change |
E. Another term for slope |
โ๏ธ Part B: Fill in the Blanks
Complete the following sentences:
- ๐ก A __________ function can be represented in the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.
- ๐ The __________ represents how much the dependent variable changes for every unit change in the independent variable.
- ๐ The __________ is the point where the line crosses the y-axis.
๐ค Part C: Critical Thinking
Imagine you're planning a road trip. Explain how you could use a linear function to estimate how much it will cost you in gas, and what factors would influence the accuracy of your estimate.