Question

How do you find the slope of `x = -3`?

Answer 1

There an undefined slope. (No slope)

Explanation:

Generally, lines have the equation of `Y=MX+B`. When that is the case, M would be the slope.

If the equation is `Y = 2x + 4`, then the slope would be 2. That line would move up two squares and over one as it went along.

However, what you have there isn't any normal line. It's a vertical line. Let's try to plot this.

To plot, I'm going to put it into my calculator (If you want to, try using www.desmos.com/calculator, its a great web plotter)

As you can see, this line is vertical! It goes directly up. We know that because the equation says that X is equal to -3. It is telling us that no matter what the Y value is, X will be -3.

For example, if Y is 4, X will be -3. If Y is 400000032, x will be -3.

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So, let's prove that a vertical line has an undefined slope.

The equation to find slope is to take two points `(A,B)` and `(C,D)` and to do the following equation:
`(D-B)/(C-A)`

So, let's take two points. Let's say that Y is equal to 3 and 2. In that case, since X is always -3, our points would be `(-3, 2)` and `(-3, 3)`.

Now, let's substitute into our formula.
`(3-2)/(-3--3) = (1)/(-3+3) = 1/0`

As you can see, the final slope is `1/0`. If you put that into your calculator, it will come out as undefined, because any number divided by zero is undefined. And so your slope for any vertical line is undefined.

Cheers!