Final answer:
A set of ordered pairs with an undefined slope signifies a vertical line where all pairs have the same x-coordinate but different y-coordinates. An example is (3, 1), (3, 4), (3, 7), (3, 10), which represents a line with the equation x = 3.
Step-by-step explanation:
To create a set of ordered pairs that will have an undefined slope, you need to understand that the slope (often represented by the letter 'm') of a line in a coordinate plane is the rate at which the y-coordinate changes with respect to the x-coordinate. Specifically, the slope is calculated as the change in y divided by the change in x (m = (Y₂ - Y₁) / (X₂ - X₁)).
When the slope of a line is undefined, it means that the line is vertical, and hence there is no change in x while there may be a change in y. This results in division by zero when calculating the slope, which is mathematically undefined. Therefore, a line with an undefined slope has ordered pairs that have the same x-coordinate but different y-coordinates. An example of such a set of ordered pairs could be (3, 1), (3, 4), (3, 7), (3, 10). All these pairs have the same x-coordinate (3 in this case) but different y-coordinates.
Remember, a vertical line like this corresponds to the equation x = a constant value (in this case, x = 3), and will not be the graph of a function due to not passing the vertical line test.