Graphing Lines
Graphing lines when the equation is in slope intercept form is super easy. The b in this formula is called the y-intercept, but you can think of it as the beginning point. You're going to take that number and plot it on the y-axis.
Next, is the slope (or how much you move to the next point) which is represented by m. This should always be a fraction, so if you have a whole number, be sure to convert it by putting it over 1. |
To use the slope, always remember rise over run! We're going to build some stair steps using the fraction. If your slope (m) is positive, go up the number of units on top of the fraction, and to the right by the number of units on the bottom of the fraction. For example, if m=4, you want to go up four units and right one unit.
One really cool thing about fractions....if you go back to your division rules (remember, the fraction bar is really a divide sign), if you divide a positive by positive, you get a positive. But you can also get a positive answer but dividing a negative by a negative. What that means is that if you go down (in a negative direction) and left (in a negative direction), you also get a positive slope. Sometimes, you'll be graphing where your count in one direction falls off the graph, so this can be really important. I like to graph one point in each direction of the y-intercept. This way, if I messed up and did went the wrong direction or in the wrong order, I can catch many mistakes if all three points don't end up on the same line.
One really cool thing about fractions....if you go back to your division rules (remember, the fraction bar is really a divide sign), if you divide a positive by positive, you get a positive. But you can also get a positive answer but dividing a negative by a negative. What that means is that if you go down (in a negative direction) and left (in a negative direction), you also get a positive slope. Sometimes, you'll be graphing where your count in one direction falls off the graph, so this can be really important. I like to graph one point in each direction of the y-intercept. This way, if I messed up and did went the wrong direction or in the wrong order, I can catch many mistakes if all three points don't end up on the same line.
Let's talk about negative slope for a minute. Just like we have two ways to get a positive answer, we have two ways to get a negative number with division. Our two choices are to have a negative on top, positive on bottom, or we can have a positive on top, negative on bottom. Again, I like to start at the y-intercept then go up and to the left as well as going back to the y-intercept to go down and to the right. If that's too confusing, you can always double check your direction by knowing what a positive and negative slope look like.
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Videos by Tarrou's Chalk Talk & Sal Kahn
Graphing Lines in Slope-Intercept Form
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Graphing Lines Using X & Y Intercepts
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Slope and Equations of Lines
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Graphing a Line in Slope-Intercept Form
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Converting to Slope-Intercept Form
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Equations of Lines and Graphing
Find Equation of Line Given Slope and Point |
Slope and Equations of Lines
Find Equation of a Line through Two Points |
Equations of Parallel and Perpendicular Lines
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These videos are copyrighted by Khan Academy & Tarrou's Chalk Talk.