📚 Topic Summary
In Grade 8 math, representing functions with simple equations is all about understanding the relationship between two variables, usually $x$ and $y$. We express this relationship as $y = f(x)$, where $f(x)$ is an equation. This equation tells us how to find the value of $y$ (the output) for any given value of $x$ (the input). Think of it like a machine: you put a number ($x$) in, and the equation spits out another number ($y$). The goal is to take descriptions or tables of these input-output pairs and write the equation that represents the relationship.
For instance, if every input $x$ is doubled to get the output $y$, the equation would be $y = 2x$. Identifying these patterns and writing them as equations is the core skill. Practice will make you a pro at turning relationships into equations!
🔤 Part A: Vocabulary
Match the terms with their definitions:
| Term |
Definition |
| 1. Function |
A. The variable whose value depends on the input variable. |
| 2. Input |
B. A mathematical rule that assigns each input value to exactly one output value. |
| 3. Output |
C. The variable that is changed in an equation or experiment. |
| 4. Equation |
D. A statement that two expressions are equal. |
| 5. Variable |
E. A symbol that represents a quantity that can vary. |
Match the term to the correct definition. (Example: 1 - B)
✍️ Part B: Fill in the Blanks
A ______ is a relationship between inputs and outputs, where each input has only one ______. We can represent this relationship with a simple ______, like $y = mx + b$, where $m$ is the ______ and $b$ is the ______. Finding these values allows us to define the function completely.
🤔 Part C: Critical Thinking
Explain, in your own words, how you can determine the equation of a line if you are given two points on that line. Give an example.