Problem 1
The slope of the line is undefined
because this line is completely vertical. All vertical lines have undefined slopes. The x coordinates are both x = p, so there is no change in the x coordinates. Note how the slope formula below leads to a denominator of 0.
m = (y2 - y1)/(x2 - x1)
m = (-a - a)/(p - p)
m = (-2a)/0
We cannot divide by zero, which is why the slope is undefined.
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Problem 2
The equation is simply x = p
The equation of any vertical line is of the form x = k, where k can be replaced with any number or expression. In this case, we replace k with p. Let's say that p = 9. This would mean x = p updates to x = 9; telling us that we have a vertical line through 9 on the x axis.
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Problem 3
There is no y intercept if p is not equal to zero. This is because any vertical line is parallel to the y axis. Parallel lines never intersect. The y intercept is where the graph crosses the y axis.
If p = 0, then the entire line overlaps the y axis (yielding infinitely many y intercepts); otherwise, if p is nonzero, then there are no y intercepts.
The answer to part 3 will depend on the status of p being nonzero or not.
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Problem 4
Answer: 0
The original line is vertical, so any line perpendicular to this original one will be horizontal. All horizontal lines have a slope of zero.
Example: the horizontal line through (2,3) and (7,3) has a slope of zero as the slope formula below shows
m = (y2 - y1)/(x2 - x1)
m = (3-3)/(7-2)
m = 0/5
m = 0
