Unit
Linear Equations and Their Graphs
MA, Stanford University
Teaching in the San Francisco Bay Area
Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts
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MA, Stanford University
Teaching in the San Francisco Bay Area
Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts
To graph a line using a table of values when given an equation of a line in standard form (Ax+By=C), start by rewriting the equation in slope-intercept form (y=mx+b). Use inverse operations to solve for y. In other words, undo what is being done to y until the y is on one side of the equal sign and everything else is on the other side. Next, step up a table of values and choose a few x values. Plug those values into the equation in order to find the corresponding y-values of the coordinate point. Plot the points on the graph. Connect the points to draw the line.
This is one of the more difficult types of graphing a line using a table because my equation is not in y equals mx plus b form. My variables aren’t as easy to work with. I can still use the table process it just might be a little trickier. So before I do any making a table, I’m going to get this equation so that y is all by itself. You’ll see in a minute why that’s going to help me.
X minus 2y equals 6 if I want to solve for y I need to undo everything that’s being done to x, excuse me that’s being done to y, step by step using my solving techniques. What I’ve done so far is subtract x from both sides now I need to divide everything by -2 so that I’ll have y equals x/2 plus -3 I’m just going to write minus 3at the end.
One last thing to think about is that x/2 is just another way of writing 1/2x so if it helps you to write it that way instead, that’s totally fine. Those are equal statements. Okay so now when I make my table of values, I’m going to be plugging in x numbers by substituting them one at a time to find their corresponding y numbers. Use some negative numbers as well as some positive numbers. I’m going to erase this now that we have the equation 1/2x take away 3 okay don’t forget that, don’t forget that y equals 1/2x take away 3. Okay so what I’m going to do is substitute in these x numbers. For example when x is-1, y is going to be 1/2 times -1 take away 3 which is -31/2. It’s going to be a little tricky to get that on the grid because of the half bit I’m just going to be in between some boxes.
Next if x equals 0, y is going to be 1/2 of 0 take away 3 which is -3. You can go through and continue in this table. I’m going to jump ahead a little bit because I’ve already done these and tell you that’s going to look like that. Now that we have our points, we’re ready to put them, on the graph and connect them using a ruler. So let’s move over to the graph and do that. My first point is going to be -1 on the horizontal axis down -31/2, -1 down one two three and a half boxes. That one doesn’t fall in one of the coordinates of the rectangle or my squares on the gird, it’s okay it’s still going to work -3, one down two and a half, over one down two and a half and then over two down two.
There it is I can kind of already tell that’s going to be a ruler straight line, ruler straight tells me that I did my table correctly and especially with fractions you want to be careful to make sure its ruler straight, so there’s my line notice how I put the arrows there to show that the line continues forever and ever in both directions. It doesn’t stop at -1 and +2 just because my graph stops there it keeps going forever and ever. So if you guys can use this table technique and if you’re able to organize your information and keep track of all your negative signs, all your fractions and stuff, you’ll be able to get perfect A+ graphs every time.