Now, Where Do I Begin?

Mr. C,

I have a question that I hope you can answer.  How can you tell exactly where the line goes on the graph? I get everything about how you can tell what the slope is, but I can't figure out where to put it on the coordinate plane. 

Can you please help me?

Best,
Sweet Lou

Good question, Lou. The best thing about this is that there is a formula. Once you know and understand this formula, you can tell not only how steep the slope is and which direction it goes, but you can tell where the slope crosses through the y-axis. This will help you know where it goes on the graph.

The formula is called slope intercept form, and it looks like this.

In this formula, you leave the x and the y. You'll understand why in a minute.

The m stands for the slope. This is usually a fraction, but sometimes it's a whole number (remember yesterday's post, where the slope was 3, and stands for 3/1). There are a few theories about why they use m for the slope, but no one really has it nailed down. Just know: m = slope!

The b stands for the y-intercept. This is very important. This tells where the line will pass through the y-axis.

So with a slope like this one...

The line would begin at the 3 on the y-axis, and from there, it would go up 4 spots and over 5 spots. Like this:

See? It's fun! Knowing your slopes doesn't have to be an uphill battle. Now you know how to chart a simple line given the slope-intercept formula.

We'll go over more slopes in future days, but for now, I hope this clears up your worries, and you can get started trying slopes. It will also become clear how these are actually useful in everyday life. (More or less.)

I hope everyone has a great day, and an amazing adventure through the wild world of mathematics.