I was challenged with this question: Explain why the formula for determining slope using the coordinated of two points does not apply to vertical lines.
This was my answer: The formula for determining a slope using two points does not apply to vertical lines simply because it would be illogical to divide by 0. To find a slope of a horizontal line we use the formulam= y1-y2/x1-x2 this stipulates that we have two points to work with.
Vertical lines have no slope. Thus, the concept of slope simply does not work for vertical lines. A vertical line will have no slope, and the slope is undefined.
A slope of 0=horizontal,
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 compute slope.
According to page 530 of the text” a two point on a vertical line have the same x coordinate, thus the change in x is always 0, always undefined. The formula for
You have some errors:
"would be illogical" should be it is not defined (not allowed) to divide by zero.
Vertical slopes have no slope. Should be vertical lines have undefined slope.
find an equation of the line containing the given pair of points (-5,-7) & (-3,-8)
To understand why the formula for determining slope using the coordinates of two points does not apply to vertical lines, we need to look at the mathematical reasoning behind it.
The formula for slope is defined as the change in y-coordinates divided by the change in x-coordinates between two points on a line. This formula is expressed as:
m = (y2 - y1) / (x2 - x1)
Now, let's consider a vertical line. A vertical line is one where all points have the same x-coordinate. For example, the equation x = 3 represents a vertical line passing through the point (3, y). In this case, no matter which two points we choose on this vertical line, the x-coordinates of both points will always be the same.
Using the formula for slope, we would have (y2 - y1) / (x2 - x1), which in the case of a vertical line becomes (y2 - y1) / (x - x). As x2 and x1 are the same, we end up with a division by zero, which is undefined in mathematics.
Mathematically, dividing by zero is not a valid operation, thus making the formula for slope undefined for vertical lines. This concept aligns with the fact that vertical lines have no slope.
To summarize, the formula for determining slope using the coordinates of two points does not apply to vertical lines because it would involve dividing by zero, which is undefined in mathematics. A vertical line has no slope, and therefore the concept of slope does not work for vertical lines.