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Graph of a Line

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Today we're going to talk about graphs of lines. So we're going to start by reviewing our coordinate plane, which is where we graph our lines. Then we'll do some examples plotting points, both from coordinate pairs and from a table. And then lastly, we'll talk a little bit about positive and negative slopes.

So let's review our coordinate plane, which is what we're going to be using to graph our lines. So our coordinate plane is made up of a horizontal number line and a vertical number line. The horizontal number line is called the x-axis, and contains x values from negative infinity all the way up to positive infinity. And similarly, the vertical number line is called the y-axis, and contains y values from negative infinity to positive infinity.

So the intersection of our two axes is something called the origin. And at the origin, both x and y are going to be equal to zero.

And any point on our coordinate plane can be written using an ordered pair or a coordinate pair. So in a coordinate pair, the first number is your x-coordinate. And your second number is going to be your y-coordinate.

So if we're looking at our origin again, the origin is going to be written as a coordinate pair as 0, 0, because again, both our x-coordinate and y-coordinate are going to be 0 at the origin.

Another example of a point on our graph written as a coordinate pair would be-- let's see. We could have negative 2 and 2. So this point here would be written as negative 2, 2 because our x-coordinate or x value is negative 2 and our y value or y-coordinate is positive 2.

So let let's see how we graph coordinate pairs onto to our coordinate plane. So my first coordinate pair is negative 4, negative 2. Remember in a coordinate pair, the first number is your x-coordinate and the second number is your y-coordinate. So to graph this point, I'm going to find negative 4 on my x-axis and find negative 2 on my y-axis. And so my point negative 4, negative 2 will be right here.

My second point is negative 2, negative 1. So again, I'll find negative 2 on my x-axis, negative 1 on my y-axis. And so negative 2, negative 1 will be right here.

My third point is 0, 0, which again remember is just our origin, or the intersection of our x and y-axes, where both x and y are equal to 0.

And then my fourth point is 2, 1, so I'll find 2 on my x-axis, 1 on my y-axis. And so my fourth point will be here. So once I've plotted my points, I can go ahead and connect them with a line.

So let's see how we can take the values from a table and plot them on a coordinate plane. So in my table, my first row are my x values. And my second row are my y values. So each set of numbers can be represented as a coordinate pair, which is how we'll graph them on our coordinate plane.

So my first pair of numbers, x is negative 2 and y is 5. So I'll go to negative 2 on my x-axis, 5 on my y-axis, and plot my point. My second pair of numbers are x is negative 1 and y is 2. So I'll go to negative 1 on my x-axis, 2 on my y-axis, and plot my point.

My third pair is x is 0 and y is negative 1. So I'll go to 0 on my x-axis, negative 1 on my--- 0 on my x-axis, negative 1 on my y-axis and plot my point. And finally, I've got x is 1 and y is negative 4. So I'll go to 1 on my x-axis, negative 4 on my y-axis, and plot my point. So now that I have my points plotted, I can go ahead and connect them with a line.

So let's talk about x- and y-intercepts. If you have the graph of a line, your y-intercept is going to be where that line intercepts with the y-axis. And your x-intercept is going to be where that line intersects with the x-axis.

So for this line, our y-intercept is going to be at the point 0, 4, because at this point, my x-coordinate is 0 and my y-coordinate is 4. My x-intercept is going to be at the point 3, 0, because my x value, my x-coordinate is 3 and my y-coordinate is just 0.

So any y-intercept is going to be written with an x-coordinate of 0, because our x-coordinate is going to be 0 everywhere on our y-axis. And then the second number will just be whatever your y-coordinate is. And similarly, our x-intercept can always be written as whatever our x-coordinate is and 0 as our y-coordinate, again because y is going to be equal to 0 everywhere on our x-axis.

So lastly, let's talk about positive and negative slopes. So when you are reading a graph, you read a graph from left to right, the same way that you read words from left to right. So if I look at this line and I start on the left side and move to the right, I can see that it's pointing towards positive infinity. So this is an example of a line that has a positive slope, again because it is going towards positive infinity on our y-axis, which is characteristic of lines that have a positive slope.

But if I look at this line, I start on the left and move to the right, I notice that it's going down towards negative infinity on our y-axis. So this is an example of a line that has a negative slope, again because as we go from left to right, it's pointing towards negative infinity on our y-axis, which is characteristic of lines that have a negative slope.

So let's go over key points from today. Make sure you get them into your notes if you don't already so you can refer to them later. A coordinate point x, y defines a location on the two-dimensional coordinate plane. Coordinate points can be connected with a line.

And the x-intercept is the location where a line or a curve intersects with the x-axis. And the y-intercept is the location where a line or a curve intersects with the y-axis. And finally, when you're reading a graph from left to right, a line with a positive slope heads towards positive infinity on the y direction. And a line with a negative slope heads towards negative infinity in the y direction.

So I hope that these key points and examples helped you understand a little bit more about graphing lines. Keep using your notes. And keep on practicing. And soon you'll be a pro. Thanks for watching.

- y-intercept:
- The location on a graph where a line or curve intersects the y-axis: (0, y)
- x-intercept:
- The location on a graph where a line or curve intersects the x-axis: (x, 0)

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