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

1 Answer
Sep 11, 2016

There an undefined slope. (No slope)


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, its a great web plotter)

enter image source here

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.


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:

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.