If you remember these concepts, you can safely skip this lesson.

The point-slope form of linear equations

If you've paid more than 10 combined minutes of attention in high school you will probably recall working with some functions of such form, known as the slope-intercept form:

But, what is this exactly?

You probably remember that you had some kind of exercise where you were given two points and had to find some equation for the line that passes through both of these two points. And those two unique variables m and c.

THIS IS NOT THE POINT-SLOPE FORM. THIS IS THE SLOPE-INTERCEPT FORM, AND YOU NEED TO KNOW THIS BEFORE IT!

This is where the slope comes in.

The m, in the form that is the equation for a line, is the slope of this line.
A slope is something that's at an angle. For example, when you go up a hill, its either a very steep hill that's impossible to climb without a crane, or you can easily walk up. This is called the slope.

Let's try to get you to understand it in a more mathematical way! Take a look at the graph of the lines I'll show you below.


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Now add 2x !

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Now make it 3x !
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As you see, the slope is, in a way, where this line is pointing, how "angled" this line in the graph is.

In another easy to understand way, the slope is a way of saying "Every time we increase x by 1, y increases by this much."

So, for x, every 1 unit we go along the x axis, we will have to also go on the y axis.
For 2x, for every 1 unit we go along the x axis, we will have to go 2 units up on the y axis!
The same for 3x.... and so on.

Obviously, if this slope is negative, then we just go down instead of up.

Now let's talk about that c.

Let's take our same x line:
center

Let's introduce that c. First, c = 1:
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Now make it 2,3,4 and so on!
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Try that with negatives too! -1, -2,-3,-4...
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In a sense, adding to that c somehow moves the graph up. The same way, subtracting from it moves it down.

This is called the y-intercept.

The value of y where it "cuts" into the y-axis.
Also, the value of y for which x is 0.

The general point-slope form of a linear equation:

Interactive Graph