📚 Topic Summary
Slope is a measure of the steepness and direction of a line. It tells us how much the $y$-value changes for every unit change in the $x$-value. We can find the slope using two points on a line, or by reading it directly from the graph of the line. Understanding slope is crucial for many concepts in algebra and beyond!
When given two points $(x_1, y_1)$ and $(x_2, y_2)$, the slope, often denoted as $m$, is calculated as: $m = \frac{y_2 - y_1}{x_2 - x_1}$. When looking at a line on a graph, slope can be determined by visually identifying the rise (vertical change) and run (horizontal change) between two points on the line, and then calculating the ratio: $m = \frac{\text{rise}}{\text{run}}$.
🧮 Part A: Vocabulary
Match the following terms with their definitions:
| Term |
Definition |
| 1. Slope |
a. The horizontal change between two points on a line. |
| 2. Rise |
b. A line that goes downwards from left to right. |
| 3. Run |
c. The steepness and direction of a line. |
| 4. Positive Slope |
d. The vertical change between two points on a line. |
| 5. Negative Slope |
e. A line that goes upwards from left to right. |
✍️ Part B: Fill in the Blanks
The slope of a line can be found using two ________ on the line. The formula to calculate slope ($m$) is $m = \frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1, y_1)$ and $(x_2, y_2)$ are the two ________. On a graph, slope is determined by the ratio of ________ to ________.
🤔 Part C: Critical Thinking
Explain in your own words why understanding slope is important in real-world applications. Give at least two examples.