Using a Graph

Many times you can use a graph to represent data in a more organized way, and in a more visual way.So, say we have the equation y = 2x-3.

What we can do is plug in a couple of numbers for x, and then find out what number we get for y, and then we can come up with some coordinates, plug them in here, and then draw a line representing the values of this equation.

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The transcript is provided for your convenience
So, we’re going to start out by plugging in 0 for x. So, I’m just putting parenthesis like that, so 2 times 0 is 0, minus 3 is -3, so y = -3. So, the first coordinate we get is x = 0, and y = -3.

Now, we’re going to plug in 5 for x, so we’re going to put 5 in parenthesis, so we get 10-3 = 7, so y = 7, so in this case, x = 5, and y = 7.
So, now, we have these two coordinates, so we can just plug these into this graph right here, and we can get a line.
And so, we have these dash marks here, so I need to go ahead and label these, so we have this x-axis, which runs horizontal, left to right, and then we have the y-axis, which runs vertical, or up and down.

So, on the right side of the y-axis, the x-axis is positive, and on the left side, it is negative. This works similarly for the y-axis. Above the x-axis, it’s positive, and below, it’s negative.

So, first, we’re going to take a look at this coordinate right here, so we have the x coordinate and the y coordinate, so we find x first, which is 0, so we’re right here, and we go down to -3, and draw a dot, and I’m going to go ahead and put the coordinates right there.

Then we look for the x coordinate first, and then the y coordinate, so we find 5, then we need to go all the way up to 7, so we’re going to need to extend this line a little bit to make it up there, and so we’re going to go from 5 all the way up to 7 and draw a dot, and then we just need to draw a line all the way up there.

If you’re using a piece of paper, you can often use a ruler. We are going to attempt to free hand this, which means the line is not going to be very straight as you can see, but we do need to write the coordinates for that too. So, then we have a line, and you can go all the way up this line and see different points on it. If x equals this certain number, then y is going to equal this certain number.

Because you can follow across here, you can go down and find the x coordinate, and then go across and find the y coordinate to figure out some other coordinates here, to figure out some other values for x and y. Here, you just have coordinates written on a page, and so, it may not mean much to you, it’s hard to visualize what that looks like, but here, you have a real visual format, an organized way to view a lot of data, and to be able to keep it and comprehend it.

Next Lesson: Linear Equations Basics