To determine the slope of a line passing through two points, we can follow these steps:
1. Determine the coordinates of the two given points. Let's call them Point1 `(0,1)` and Point2 `(3,1)`.
2. Calculate the difference in y-coordinates (Delta_Y) of the two points. This is done by subtracting the y-coordinate of Point1 from the y-coordinate of Point2. In this case, Delta_Y will be 1 - 1, which equals 0.
3. Calculate the difference in x-coordinates (Delta_X) of the two points. This is done by subtracting the x-coordinate of Point1 from the x-coordinate of Point2. Here, Delta_X will be 3 - 0, which equals 3.
4. If Delta_X is not zero, then calculate the slope. The slope of a line (commonly noted as m) is the ratio between Delta_Y and Delta_X. So, m = Delta_Y/Delta_X. In our case, the slope is 0/3 which simplifies to 0.
So, the differences in the y-coordinates and x-coordinates are 0 and 3, respectively, and the slope of the line passing through the points `(0,1)` and `(3,1)` is 0. This indicates that the line is horizontal.