Question

A line passes through the points (P, a) and (P, –a) where P and A are real numbers and P does not equal 0. Describe each of the following. Explain your reasoning.

1. slope of the line

2. equation of the line

3. y-intercept

4. slope of a line perpendicular to the given line

Answer 1

9514 1404 393

Answer:

1. undefined
2. x = P
3. does not exist
4. 0

Explanation:

2. The x-value of the given points is the same, so the points both lie on the vertical line ...

x = P

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1. The slope of a vertical line is "undefined".

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3. Given that P ≠ 0, the vertical line is parallel to the y-axis, so there is no y-intercept.

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4. A line perpendicular to a vertical line will be horizontal. A horizontal line has a slope equal to zero.