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How to Graph Equations with Slope Intercept Form

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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.

 


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.

 

If you have any suggestions for future lessons, e-mail us at podcast@yourtutoronline.com.

 

If you need more help with this or other topics, visit www.yourtutoronline.com to find a tutor or just send an e-mail to tutor@yourtutoronline.com. We provide online tutoring services in the virtual classroom you just saw on this video. Be sure to subscribe to our podcast in iTunes to get the latest videos. I’ll see you next time. Thanks for watching. Class dismissed.

Written by Joel

April 17th, 2008 at 7:31 pm

Posted in Lessons

17 Responses to 'How to Graph Equations with Slope Intercept Form'

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  1. THIS was soo helpful.
    Keep up the work =)

    Jessica

    14 Jul 08 at 8:40 am

  2. Thanks for the comment. It’s good to know that you are finding the videos helpful.

    YourTutorOnline

    14 Jul 08 at 9:03 am

  3. WOW!!
    lOl
    YOU
    SHOW ME
    BETTER
    THEN
    MY TEACHER
    dOES…
    KEEP iT UP iTE SO
    i CAN, qET ON THiS
    WEBSiTE LATELY Nd
    LEARN && DO MY HOMEWORK
    jeje
    CUZ i FOUNdEd THiS
    WEbSiDE Nd NOW
    IM DOINq MY
    HOMEWORK!!!
    =]]
    →[♥]←

    SANDii

    23 Sep 08 at 7:38 pm

  4. this helped me with my homework, ty!!!!!!!

    math dawg

    12 Nov 08 at 3:20 pm

  5. Thank you so much, now I can actually do my homework when before I had NO idea!!
    THANK YOU! :]

    Alondra

    4 Dec 08 at 10:11 pm

  6. This helped me lot with my project. At first I was confused when my teacher taught me but sense I found this website I completely understood it. I’m sooo going to get an A+!!!!!

    samantha

    29 Jan 09 at 3:02 pm

  7. Thnx this really worked out great for me =)

  8. I needed a refresh on graphing slops..this was PERFECT. Thanks for doing Pos and Negative.

    CC

    30 Aug 09 at 9:27 pm

  9. I love this web site now, its on my favorites just in case i have a question that need’s solving, lol. Keep this web site up & running please !!!

    stuart williams

    26 Nov 09 at 11:10 am

  10. You are a life saver, thanks a bunch!!!!

    zak

    9 Dec 09 at 8:39 pm

  11. y=2/5X=2

    GRAPH THE FOLLOWING LINES USE ANY METHOD TABLE OR SLOPE – INTERCEPT

    JANINE

    20 Apr 10 at 5:52 pm

  12. ANOTHER I HAVE A QUESTION ON

    2Y-9X=14

    GRAPH THIS LINE

    JANINE

    20 Apr 10 at 5:53 pm

  13. THANK YOU SOOOOOOOOOO MUCH!!!! now I finally understand! Oh, my Dad taught me another method by replacing the y with a 0 or some number, can you show an example of this too?

    Moogle

    1 Dec 10 at 4:20 pm

  14. @Moogle
    Yes, thanks for the suggestion I think I will make a video on that. Replace x with zero and then solve for y that gives you your y intercept. Thanks so much for your suggestion, I am always looking for idea for videos people want to see.

    Joel

    2 Dec 10 at 9:19 am

  15. Thank you! I have math first hour, so by the time I get to my homework, I forget how to do it. Hopefully I will be able to boost my grade up to an A on the next test, because I actually understand it!
    Oh, and I need to write an equation of a line shown on a graph, can you make a video for that?
    Thank you!

    madison

    11 Oct 12 at 7:19 pm

  16. thanks so much for this. it was a really helpful refresher for geometry. but my teacher tells me that when you do slope intersect form
    , for example y=3x+4, in order to graph it you do an xy chart with 0, a possitive number and a negative number. i’m very confused on that part because my algebra teacher did not teach us this last year. can you do a video on that way too? thanks :)

    XxkaylaxX

    1 Nov 12 at 5:16 pm

  17. @Janine, you have to get Y by itself. First add 9x to both sides

    2y-9x=14
    2y-9x+9x=9x+14
    2y=9x+14
    – —– (This means divide)
    2 2
    y=9/2x=7

    Hope this helped.

    LoveGaga

    3 Dec 12 at 5:07 pm

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