What is an equation of the line that passes through the points (-6, 3) and (-6, 6)?

Question

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Answer 1

I can see why you're having a difficult time answering this one. This is kind of a a trick question.

First we would like to find the slope. Remember the slope equation:

m=(y₂-y₁)/(x₂-x₁)

Using the points given, we have:

m=(6 - 3)/(^-6 - ^-6) = 3/0

But remember, we're not allowed to divide by zero! So this line doesn't have a slope. Another way to say that is that the slope is undefined.

Do you recall what type of lines have an undefined slope? These would be the vertical lines, and vertical lines have an equation with only x.

So the equation of the line is x = ^-6.

Does that make sense?

Answer 2

This line is not moving anywhere left or right. Imagine or graph the points. For any y the x is -6 . So x = -6 is an equation for a line that goes straight up and down at that point. The slope is "infinite"/undefined (undefined is more formal/correct) which may be why you're having trouble.

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Answer 3

If you plot these points in the coordinate plane and connect the two points you will find you have a vertical line. The slope of a vertical line is undefined.