The Shortest Distance Between Two Points

Dear Mr. C, 

I'm trying to figure out how I can tell the slope if someone just gives me two coordinate points. I asked my math teacher, but I three of my friends Snapchatted me while she was answering, so I had to read them, and then she got all mad because I was looking at my phone instead of listening, which is totally unfair and dumb, because she doesn't understand about Snapchat. 

Whatever,

Jen Snodgrass

Well, Jen, I sure hope you're ready to read something other than Snapchat messages, because I'm about to lay some knowledge on you.

Let's say that your teacher gives you these two points: (2,1) and (4,7). Simply plot those points.

Then, draw the line between them, and then see how far across you have to go, and then how far up you have to go in order to get from one to the other.

You can see that this one went over 2 spaces, and up 6 spaces. Since slope is always written as rise over run, this one goes up 6, and over 2. Therefore, the slope is 6/2.

Of course, we always want to simplify our fractions, so 6/2 is equal to 3/1, and that simplifies all the way down to 3.

The slope of this line is 3!

Now, let's say your two points head in a downward direction. You will remember from yesterday's post that this would indicate a negative slope.

If they gave you (3,8) and (8,6), you would still put the dots in their place and draw the line between them.

You can see that this one goes across 5 spaces, and down 2 spaces. So, "rise" over run would indicate that this one has a slope of -2/5.

In this case, "rise" over run was actually "drop" over run, but it still works the same. It's just negative!

So there you have it, Jen. Hopefully you will put down the phone and listen, because your teacher is most likely a pretty smart lady.

Until tomorrow, I hope everyone has a fantastic day and that you will find that math is all around you. It helps to speak the language!