This was the question : Explain why the formula for determining slope using the coordinates of two points does not apply to vertical lines.

This is my answer:The formula for determining a slope using two points does not apply to vertical lines simply because dividing by 0 is not allowed…it is undefined. To find a slope of a horizontal line we use the formula m=y1-y2/x1-x2 this stipulates that we have two points to work with.
Vertical lines are in the form of x=some number, such as x=6; When a line involves an undefined slope the line is vertical, and when a line is vertical you will end up dividing by 0 if you try and evaluate the slope.
Vertical lines have undefined slopes. Thus, the concept of slope simply does not work for vertical lines. A slope of 0=horizontal,
According to page 530 of the text” any two points on a vertical line have the same x coordinate, thus the change in x is always 0, always undefined.

Is this right? If so, do you have any suggestions to make it less wordy and redundant

Your explanation is correct, but there are some suggestions to make it less wordy and redundant:

The formula for determining the slope using two points, m = (y2 - y1) / (x2 - x1), cannot be used for vertical lines because it involves dividing by zero, which is undefined. The formula requires two distinct points to calculate the change in y divided by the change in x.

Vertical lines, on the other hand, have the equation x = some number (e.g., x = 6). These lines have an undefined slope because any two points on a vertical line will have the same x-coordinate. Therefore, the change in x is always zero, resulting in a division by zero when attempting to evaluate the slope. Hence, the concept of slope simply does not apply to vertical lines.

To summarize, the formula for determining slope using two points is not applicable to vertical lines because dividing by zero is undefined, and the change in x for vertical lines is always zero.