๐ Topic Summary
Slope is a measure of how steep a line is. It tells us how much the $y$-value changes for every unit change in the $x$-value. Think of it like climbing a hill โ the steeper the hill (the greater the slope), the more effort it takes to climb for every step you take forward. We usually represent slope with the letter 'm'. The slope can be found using two points on a line, $(x_1, y_1)$ and $(x_2, y_2)$, using the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$. Understanding slope is crucial for many things, from designing ramps to predicting trends!
๐ Part A: Vocabulary
Match the terms with their definitions:
| Term |
Definition |
| 1. Slope |
A. The point where the line crosses the y-axis. |
| 2. Rise |
B. The change in y-values between two points. |
| 3. Run |
C. A line with a slope of zero; horizontal. |
| 4. Y-intercept |
D. The change in x-values between two points. |
| 5. Horizontal Line |
E. The measure of steepness of a line. |
Write the correct letter (A-E) next to the term number:
- Slope: ___
- Rise: ___
- Run: ___
- Y-intercept: ___
- Horizontal Line: ___
โ๏ธ Part B: Fill in the Blanks
Complete the paragraph using the words below:
(positive, negative, zero, undefined, steepness, coordinates)
The slope of a line describes its __________. A line that goes upwards from left to right has a __________ slope. A line that goes downwards from left to right has a __________ slope. A horizontal line has a __________ slope, while a vertical line has an __________ slope. To calculate slope, we use the __________ of two points on the line.
๐ค Part C: Critical Thinking
Explain in your own words how the slope of a line can be used to determine if two lines are parallel or perpendicular.