Final Answer:
The slope of a line can be calculated using the slope formula with any set of ordered pairs that lie on the line.
Step-by-step explanation:
The slope of a line represents the rate at which it rises or falls as it moves from one point to another. The formula for calculating the slope of a line between two points, (x1, y1) and (x2, y2), is given by: slope = (y2 - y1) / (x2 - x1). This formula measures the change in the y-coordinates divided by the change in the x-coordinates between two points on the line.
When determining the slope of a line, any pair of ordered points that belong to the line can be substituted into the slope formula. For instance, if you have points (3, 5) and (7, 11) on a line, you can calculate the slope by using these ordered pairs in the formula: slope = (11 - 5) / (7 - 3) = 6 / 4 = 1.5.
Similarly, if you have different points like (-2, 4) and (1, 7) on the same line, you can substitute these coordinates into the slope formula: slope = (7 - 4) / (1 - (-2)) = 3 / 3 = 1. This demonstrates that regardless of the specific ordered pairs chosen from the line, the resulting slope value remains constant.
Hence, any set of ordered pairs that are part of the line can be used interchangeably in the slope formula to determine the slope of the line accurately.