📚 Topic Summary
Slope is a measure of the steepness of a line. It tells us how much the $y$-value changes for every unit change in the $x$-value. A positive slope indicates an increasing line, a negative slope indicates a decreasing line, a zero slope indicates a horizontal line, and an undefined slope indicates a vertical line. We can calculate slope using the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ where $(x_1, y_1)$ and $(x_2, y_2)$ are two points on the line.
We can also determine slope directly from a graph by counting the 'rise over run,' or find it from a table by looking at the constant rate of change between $x$ and $y$ values.
🧮 Part A: Vocabulary
Match each term with its correct definition:
- 📐 Term: Slope Definition: The steepness of a line.
- 📈 Term: Rise Definition: The vertical change between two points on a line.
- 🏃 Term: Run Definition: The horizontal change between two points on a line.
- ➕ Term: Positive Slope Definition: A line that increases from left to right.
- ➖ Term: Negative Slope Definition: A line that decreases from left to right.
✍️ Part B: Fill in the Blanks
Complete the paragraph using the words: rise, run, slope, points, equation.
The ________ of a line can be calculated if we know two ________ on the line. We use the ________ over ________ method, which is represented in the slope ________. This calculation tells us how steep the line is.
🤔 Part C: Critical Thinking
Explain in your own words how you can determine the slope of a line from a graph and from a table. Give an example of each.