Question
Draw a line representing the rise and a line representing the run of the line. State the slope of the line in simplest form.
Answers
GPT-4o mini
To illustrate a line representing the rise and run, consider a line on a coordinate plane where:
- **Rise**: The vertical change between two points on the line.
- **Run**: The horizontal change between the same two points.
Let's say we choose two points on the line: Point A (2, 3) and Point B (5, 7).
1. **Calculate the Rise**:
\[
\text{Rise} = y_2 - y_1 = 7 - 3 = 4
\]
2. **Calculate the Run**:
\[
\text{Run} = x_2 - x_1 = 5 - 2 = 3
\]
3. **Find the Slope** (\( m \)) of the line:
\[
m = \frac{\text{Rise}}{\text{Run}} = \frac{4}{3}
\]
Thus, the slope of the line in simplest form is **\( \frac{4}{3} \)**.
If you were to visualize it, you could draw a right triangle where the vertical line represents the rise of 4 units, and the horizontal line represents the run of 3 units, with the hypotenuse being the line itself.
- **Rise**: The vertical change between two points on the line.
- **Run**: The horizontal change between the same two points.
Let's say we choose two points on the line: Point A (2, 3) and Point B (5, 7).
1. **Calculate the Rise**:
\[
\text{Rise} = y_2 - y_1 = 7 - 3 = 4
\]
2. **Calculate the Run**:
\[
\text{Run} = x_2 - x_1 = 5 - 2 = 3
\]
3. **Find the Slope** (\( m \)) of the line:
\[
m = \frac{\text{Rise}}{\text{Run}} = \frac{4}{3}
\]
Thus, the slope of the line in simplest form is **\( \frac{4}{3} \)**.
If you were to visualize it, you could draw a right triangle where the vertical line represents the rise of 4 units, and the horizontal line represents the run of 3 units, with the hypotenuse being the line itself.