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.
A quick look, I just need to know if this was answered correctly?
Yes, your explanation is correct. To make it less wordy and redundant, you can consider the following revisions:
"The formula for determining slope using the coordinates of two points does not apply to vertical lines because it involves dividing by zero, which is undefined.
When we calculate the slope using the formula m = (y1 - y2)/(x1 - x2), it assumes that we have two distinct points with different x-coordinates. However, vertical lines are represented by equations of the form x = some number, such as x = 6. In these cases, all the points on the vertical line have the same x-coordinate, making x1 equal to x2 in the formula.
This leads to a denominator of zero, and division by zero is not allowed in mathematics. Therefore, the slope is undefined for vertical lines.
In summary, the concept of slope does not apply to vertical lines because the formula requires dividing by zero, which is not permissible."
By making these revisions, the explanation becomes more concise and eliminates redundancy while still conveying the necessary information.
Yes, your explanation is correct in stating that the formula for determining slope using two points does not apply to vertical lines because dividing by 0 is not allowed, resulting in an undefined value. However, I'll provide you with a more concise and less redundant explanation:
The formula for slope involves the difference in the y-coordinates divided by the difference in the x-coordinates of two points on a line. This formula, \(m = \frac{{y_2 - y_1}}{{x_2 - x_1}}\), is valid for any non-vertical line.
However, when we consider a vertical line, every point on that line will have the same x-coordinate. This means that the difference in x-coordinates, \(x_2 - x_1\), will always be 0. Dividing by zero is undefined in mathematics, so we cannot apply the slope formula to vertical lines.
Hence, the concept of slope does not work for vertical lines, and their slopes are considered undefined. Meanwhile, a slope of 0 represents a horizontal line.