Hi. This is Anthony Varela. And today we're going to be talking about the graph of a line. So we're going to be talking about the coordinate plane. Then we'll practice plotting some points on a line, and then we'll talk a little bit more about slope and intercepts of a line on a graph.
So first we're going to talk about the coordinate plane. And the coordinate plane is a grid, so graph paper would be a good example of a coordinate plane. And the coordinate plane has two axes to it, which resemble number lines. So we have a horizontal number line that goes from negative infinity to positive infinity, and then we also have a vertical number line also from negative infinity up to positive infinity.
Now we call the horizontal number line the x-axis, and we call the vertical number line the y-axis. And where these two axes intersect we call the origin. Notice that this intersection point, x, is neither negative nor positive, and the same thing with y. Y is neither negative nor positive. So we say that the origin has a coordinate point or coordinate location of 0, 0. So the coordinate plane is a horizontal number line and a vertical number line intersecting at the origin, 0, 0.
So talking about the origin being located at 0, 0 gets into a discussion, then, about a coordinate pair. Well a coordinate pair is a pair of x value and a y value that describe a location on the grid. So we always write our x-coordinate first, and then we write our y-coordinate. We put a comma between and put them in parentheses to show a coordinate pair.
So x represents horizontal position along this horizontal number line, and y represents the vertical position along the vertical number line. So here is a point on the graph, the point 2, 5. And so this coordinate point 2, 3, says that this is the intersection of x equals 2 and y equals 5. So here is the coordinate point 2, 5.
So let's practice plotting some points on a line. I have a couple of different coordinate pairs, and we're going to plot these on our graph. So looking at this first one, negative 1, 1. I'm going to start at the origin, and I'm going to find negative 1 on the x-axis. I'm going to find positive 1 on the y-axis. And this is the intersection of those two points. So negative 1 and 1.
My next point, I'm going to plot 3 comma 7. I'm going to locate 3 on the x-axis right here. I'm going to locate 7 on the y-axis right here. So the intersection of x equals 3 and y equals 7 is right here. That's the point 3, 7.
Let's go ahead and plot 1 comma 4. So I'm going to find 1 on the x-axis, find 4 on the y-axis. So the coordinate point 1, 4 is right here. And last point, negative 3, negative 2. So I'm going to start at the origin. Find x equals negative 3, so negative 1, negative 2, negative 3. And find y equals negative 2. So the point, then, would be the intersection of y equals negative 2, and x equals negative 3. And I said it backwards. I should say x equals negative 3 and y equals negative 2.
So now what we can do is we can connect the dots to reveal a line, and lines are infinite, so I'm just going to take a moment to extend my line. So there, we have a line that follows on all the points we just plotted.
We can also plot points from a table of values. So here we have a column of x values, here we have a column of y values. So together, each row then represents a coordinate pair, an x value and an associated y value. So to plot this point here, we're going to find negative 6 on the x-axis and positive 5 on the y-axis right here. So here is the point, then, negative 6, 5.
Our next point, negative 2, 3. We're going to find negative 2 on the x-axis, positive 3 on the y-axis. There's the point, negative 2, 3. Our next point, finding positive 2 on the x-axis, positive 1 on the y-axis. So there is the point 2, 1. And lastly, starting at the origin, finding 6 on the x-axis, and here's negative 1 on the y-axis. So the point 6, negative 1 is right there. And once again, we can connect all of these dots to reveal a line on our graph that passes through all the points.
So next, I'd like to talk about intercepts on a graph. And there are two intercepts that we see here. We have a y-intercept and an x-intercept. Now the y-intercept is the location on a graph where a line or curve intersects the y-axis. So I think y-intercept intersecting the y-axis. The x-intercept is the location on a graph where a line or curve intersects the x-axis. So x-intercept intersects the x-axis.
So here are those intercepts plotted on the graph. This point right here is the y-intercept because it intersects the y-axis. And notice that this occurs when x equals 0. So very generally, any x-intercept is going to have a coordinate 0 comma y, whatever this y value may be.
Now the x-intercept is right here, where the line crosses or intersects the x-axis. And notice this occurs when y equals 0. So generally, all x-intercepts have some coordinate x-- whatever that may be-- but the y-coordinate will always be 0. So with intercepts, the y-intercept has an x-coordinate of 0, and the x-intercept has a y-coordinate of 0.
Lastly, I'd like to talk about slope, but we're not going to get into too much mathematical detail. All I want to do is talk very briefly about what slope is, and then I'm going to show you positive and negative slope. So the slope can be thought of as the steepness of a line. And it could be positive, it could be negative. There are other possibilities too that we're not going to get into in this lesson.
But thinking about what a positive slope looks like, the positive slope line is right here. It's the blue line. And when we're reading our graph from left to right, so as x is going towards positive infinity, taking a look at our y value that's also increasing. So y increases with x, so that's a positive slope.
Our green line, however, if we're reading our graph left to right, so as x increases, our y value is actually going down, heading towards negative infinity. So that's why we describe this line as having a negative slope. So the slope is the steepness of a line, and this line right here has a positive slope, this line right here has a negative slope.
So let's review the graph of a line. Well, we talked about the coordinate plane being a horizontal number line and a vertical number line intersecting at the origin, which has coordinates 0, 0. So a coordinate pair has an x-coordinate and a y-coordinate. X refers to horizontal position, y refers to vertical position.
We talked about intercepts on a graph. The y-intercept is where the line crosses the y intercept, has an x-coordinate of 0. The x-intercept intercepts the x-axis, so it has a y-coordinate of 0. And lastly, we talked about slope being the steepness of a line. We saw an example of a line with a positive slope and a line with a negative slope. So thanks for watching this video on the graph of a line. Hope to see you next time.