How to Graph Equations with Slope Intercept Form

In this lesson we will learn about the slope intercept formula. We look at what slope and intercept mean as well as how to graph the equation.

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transcript

Welcome to Your Tutor Online video podcast. In this lesson we'll learn about slope intercept form of a line.

The slope intercept form of a line helps to graph equations. The formula is y = mx + p. x and y are just going to be points in the line. m is the slope. p is the intercept. Here is an example equation for a line. y = 2x + 3. You can tell what each part of the equation is based on its position in the formula. The slope is 2, because it's in the first spot. And the intercept is +3, because it's in the second place.

Let's look at slope. Slope means rise over run. Always think of it as a fraction. When slope is a whole number like in our example, it can be rewritten just with a denominator of 1. 2 over 1. The top number of the fraction is rise, and the bottom number of the fraction is run. We normally go up and to the right. If any part of the slope is negative, we'll go on an opposite direction. So let's start with this point. If we had a slope of 2 we go up 2 over 1, up 2 and over 1. Slope talks about how each point on the line is in relation to another.

Next let's look at y-intercept. It's the last number in the equation and just means where the line crosses the y-axis. For example, it's +3, so just put a dot at positive 3 on the y-axis and that's the line that goes up and down. And we know that this equation is some line that passes through that point. If the y-intercept is negative, we will just put the dot at the negative part on the y-axis.

Now that we know about the slope and the intercept individually, we need build up those two things together. We're still going to use our example y = 2x + 3. To graph this we're going to start with the y-intercept. It's going to go on the y-axis, the up and down line at +3, (one, two, three) and put a dot.

Now we're going to work with our slope. It's 2. Remember that means 2 over 1, rise 2, run 1, up 2, (one, two) over 1 and put our second dot. And we'll repeat the process one more time, (one two), and over 1. All three those points are on our line. Now I just want to connect them with a single line. And here is our line y = 2x +3.

I want to give you one more example before we finish today. And this equation involves negative numbers so you can see how to handle those on the graphing. y = -2/3x - 2. Again we're going to start with the y-intercept at -2 and go to -2 on the y-intercept and put a dot.

This time our slope is -2/3. So we're going to rise -2, just the same thing as going down and then run 3. So down 2, (one, two) and run 3. I'm still going to move to the right (one, two, three). Repeat the process one more time, down 2, (one, two). Run 3 (one, two, three). Three points should be enough, so I'll connect my dots. And there's our line.

One thing I forgot to show you in the last example is we need to add little arrows on either end of our line to show that it continues on forever.

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