multiple representation of linear functions

By starting the table off at zero on the left side with your X, you'll see what the Y intercept this time would be a three. Another thing you need to pay attention to when you're creating a table is that for your ex column, you need to try to count by ones, zero, one, two, three, four, 5, 6, 9. Because what that's going to do is it's going to allow you to see what the pattern is on your Y column. The pattern this time is a simple addition. Three plus one is four, four plus one is 5. 5 plus one is 6. So the pattern for the Y column is going to be a plus one. And when we talk about whether the pattern is going to be linear or not, all linear functions are either addition or subtraction. And since this is adding one every time, it is a linear function. What we've then can do is take this table and turn it into a graph. This graph represents the table over here to the left. Each of your corner points on the table zero three are represented by a dot on the graph. And what we're going to do is we're just going to take each of these corner points and plot them over here to the right side. 

So when X is one, your Y becomes a four, and we're going to move it all the way over. When you have a two, your Y is going to be a 5, which will move that right over there. And then when X is a three or Y is a 6, which is going to be the very last one we have way up there. Once we plot your points as a couple things we need to make sure to notice. You always want to check to make sure that your scale is correct on your table. The scale tells you the numbers that go down your X and your Y axis. The scale for this one on the bottom is going to need to be in a constant pattern. Skip one one, skip one, two, skip one three. The same thing going up here, this time the scale is counting by twos every other. Skip one two, skip one four, skip one 6, skip one 8. This is a constant pattern for your scale, which is appropriate. What we're able to do once we make a graph out of the table is we're able to predict what some of the future points would be as we extend the line outward. 

Again, because it's a linear function, we are able to continue to draw this line if we need it to, just like we would be able to add rows to the table on down. 345-612-3456, and we'd be able to tell where all the points on this graph belong. Another way that we're going to be building linear functions is through an equation, and there are two parts. On the left side, you have the X variable, and then on the right side, you have a number. Again, because this is a linear function, this is going to be the left side which is going to be what we call the pattern or the coefficient. The coefficient is always going to be the number next to the variable X we're also going to call the pattern because again, remember over here we found that the pattern with a plus one. Because the pattern was a plus one over here, that's where the gray one right here becomes. 

The next thing we're looking for is the Y intercept. The Y intercept is this whole number over here. It tells you where the graph starts at. Over here, you can see that the graph started at plus three. Over here, you can also see that the graphs started at plus three. So your Y intercept for this one is going to be a plus three.