To illustrate the concepts of "rise" and "run" in the context of a line on a graph, let's consider a coordinate system:
- "Rise" refers to the vertical change between two points on a line. It can be visualized as the height difference between these two points.
- "Run" refers to the horizontal change between the same two points. It can be visualized as the horizontal distance between them.
If we have two points on a line:
- Point A: (1, 2)
- Point B: (4, 5)
We can calculate the "rise" and the "run" as follows:
- Rise: The change in the y-coordinates = \(y_2 - y_1 = 5 - 2 = 3\)
- Run: The change in the x-coordinates = \(x_2 - x_1 = 4 - 1 = 3\)
Now, we can find the slope of the line, which is defined as the ratio of the "rise" to the "run":
\[ \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{3}{3} = 1 \]
The slope of the line in simplest form is 1.
In a graphical representation, you would have an upward diagonal line when plotting points A and B, with the rise indicated by the vertical distance and the run indicated by the horizontal distance.