This was the question: Explain why the formula for determining slope using the coordinates of two points does not apply to vertical lines.
The formula for determining a slope using two points does not apply to vertical lines simply because dividing by 0 is not allowed…undefined. To find a slope of a horizontal line we use the formula m= y1-y2/x1-x2: this specifies 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 using points (-4,5) and (8,-5):
m= (5)-(5)/ (8)-(-5) =0/-13; undefined
All the points on a vertical line hold the same x coordinate, so x1= x2 and the denominator of the slope formula is zero. For that reason, the slope is undefined because division by zero is not allowed.
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.
It is correct but too wordy for me. This would have been enough, in my opinion. All the words are yours:
<<The formula for determining a slope using two points does not apply to vertical lines because dividing by 0 is not allowed…undefined. To find a slope of a horizontal line we use the formula m = (y1-y2)/(x1-x2)
All the points on a vertical line hold the same x coordinate, so x1= x2 and the denominator of the slope formula is zero. For that reason, the slope is undefined because division by zero is not allowed.>>
Thank you
If you try and evaluate the slope using points (-4,5) and (8,-5):
m= (5)-(5)/ (8)-(-5) =0/-13; undefined
I might point out that 0/-13 is not undefined. You are not dividing by zero; in this example you are dividing by -13. Another example, as DrWLS points out, being too wordy can come back to bite you.
like this: The formula for determining a slope using two points does not apply to vertical lines simply because dividing by 0 is not allowed…undefined. To find a slope of a horizontal line we use the formula m= y1-y2/x1-x2: this specifies 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.
Using points (5, 8): and (5,-4): m= (8)-(-4)/ (5)-(5) = -12/0 is; undefined
All the points on a vertical line hold the same x coordinate, so x1= x2 and the denominator of the slope formula is zero. For that reason, the slope is undefined because division by zero is not allowed.
Yes, your explanation is correct. However, to make it less wordy and redundant, you can try the following revised explanation:
The formula for determining slope using the coordinates of two points cannot be applied to vertical lines because dividing by zero is not allowed and results in an undefined value. In the formula m = (y1 - y2) / (x1 - x2), we need two distinct points to calculate slope. When a line is vertical, it is in the form of x = some number, such as x = 6. This means that all the points on the line have the same x coordinate. As a result, x1 = x2, and the denominator of the slope formula becomes zero. Division by zero is undefined in mathematics, so the slope for a vertical line is undefined. Therefore, the concept of slope does not work for vertical lines. On the other hand, a slope of 0 is associated with horizontal lines. According to the text, any two points on a vertical line have the same x coordinate, resulting in a change in x of 0, which is always undefined.