[MUSIC PLAYING] Let's look at our objectives for today. We'll start by reviewing graphs and equations. We'll then look at what slope intercept form equations look like. We'll look at the slope and y-intercept on a graph. And finally, we'll do some examples graphing slope intercept form equations.
It's often useful to graph equations in order to visually represent the relationship between variables. In order to graph a line, you only need to find at least two points on the line. There are many ways to graph a line. One strategy might be to pick two values for x and find their corresponding y values to plot the points, and another strategy is to write an equation in a certain form to easily identify important information about the line.
Let's look at slope intercept form equations. The slope intercept form of an equation can be used to more easily graph a line. Equations in slope intercept form look like this, y equals mx plus b. y equals mx plus b is called "slope intercept form" because we can easily identify the slope and the y-intercept of the line.
In this equation, the variable m represents the slope of the line. Recall the slope of a line as the steepness of a line. We find the slope by dividing the change in y-coordinates by the change in x-coordinates, so we can also think of slope as rise over run. The variable b in the equation represents the y-intercept of the line. The coordinate point of the y-intercept is 0, b, and the y-intercept is the location on a graph where a line or a curve intersects the y-axis.
Now, let's look at the slope and y-intercept on a graph. The equation of the graph below is y equals 2/3 x minus 1. On the graph, we can see that the y-intercept is negative 1, which corresponds to the negative 1 value of b in our equation. The slope of the line can be found by finding the rise over the run.
Starting from the y-intercept, we locate the next easily identifiable point on the line. Then from the y-intercept, we see that we rise 2 and have a run of 3 in the positive direction. So the slope is 2 over 3, which corresponds to the m value in our equation.
Let's look at another equation in slope intercept form. We have y equals 1/5 x plus 2. Let's see how to graph this equation.
We start by identifying the y-intercept, which is the b value. So the y-intercept is 2 and at the coordinate point 0, 2 on the graph. So here is our y-intercept.
Then looking back at our equation, we look for the slope, which is the m value. The slope is 1/5, so the rise is 1 and the run is 5. Starting from a y-intercept, this means we go up 1 and over 5 in the positive direction to find a second point.
Finally, we can connect the points to create a line representing the equation. Here is another example. We have y equals negative 3x plus 6. To graph, we start by identifying the y-intercept, which, again, is the b value. So the y-intercept is 6 and at the coordinate point 0, 6 on the graph.
Then looking back at our equation, we look for the slope, which is the m value. The slope is negative 3, which we can write as a fraction, negative 3 over 1, which means the rise is negative 3 and the run is 1. Starting at our y-intercept, this means we go down 3 and over 1 in the positive direction to find a second point. Finally, we connect the points to create a line representing the equation.
Let's go over our important points from today. Make sure you have these in your notes so you can refer to them later. In order to graph a line, you only need to find at least two points on the line.
Equations in slope intercept form look like this. y equals mx plus b. y equals mx plus b is called "slope intercept form" because we can easily identify the slope and the y-intercept from the equation. The y-intercept is the b value in the equation and is the point where the line crosses the y-axis. The slope is the m value in the equation, and we think of slope as rise over run between any two points on the line.
So I hope that these key points and examples helped you understand a little bit more about graphing a line using slope intercept. Keep using your notes, and keep on practicing. And soon, you'll be a pro. Thanks for watching.