It looks like you're asking for help with a coordinate system involving the concepts of "rise" and "run," which are essential parts of calculating the slope of a line in a graph. Here's how you can visualize it and determine the slope:
- Rise refers to the vertical change between two points on the line (how much the line goes up or down).
- Run refers to the horizontal change between those two points (how much the line goes left or right).
To find the slope (m) of the line, you use the formula: \[ m = \frac{\text{rise}}{\text{run}} \]
Example:
Suppose you choose two points on your line:
- Point A (2, 3)
- Point B (5, 7)
Now, you can calculate the "rise" and "run":
-
Rise:
- The change in y-coordinates: \( 7 - 3 = 4 \)
-
Run:
- The change in x-coordinates: \( 5 - 2 = 3 \)
Slope Calculation:
Now, plug the values into the slope formula:
\[ m = \frac{4}{3} \]
This slope \( \frac{4}{3} \) is already in its simplest form.
To visualize this, you would draw:
- A vertical line segment (rise) measuring 4 units up.
- A horizontal line segment (run) measuring 3 units to the right from the end of the rise.
You may draw these lines on graph paper or a coordinate grid, ensuring that the coordinates of your chosen points match.
If you have specific points or would like to create a different example, please provide them, and I can help further!