Hi, this is Anthony Varela. And today, we're going to be graphing linear equations. So for our first example, our equation is going to be in slope-intercept form. For our second example, we're going to be graphing a line written in point-slope form. And our last example, our equation will be in standard form.
So for our first example, we want to graph the line y equals 5/2x minus 2. So this is written in slope-intercept form, y equals mx plus b. So m is the slope of the line. And b is the y-intercept. So a great starting point is to go ahead and plot our y-intercept. We can see that this is negative 2. And the y-intercept is where our line crosses the y-axis. So it's going to be negative 2 on the y-axis. So there is our y-intercept.
And now, we can start at our y-intercept and use slope to identify other points on our line. So our slope can be thought of as rise over run. So rise is 5 and run is 2. So I'm going to start at my y-intercept and go up 5, so 1, 2, 3, 4, 5, and over 2. This is another point on my line.
And I can do this again-- up 1, 2, 3, 4, 5, over 2. And I'm just going to go ahead and then extend it in the other direction. So this then is the graph of the line y equals 5/2x minus 2.
In our second example, here we went to graph the line y minus 6 equals negative 2 times x minus 3. So this is given to us in point-slope form-- y minus y1 equals m times x minus x1. So here, we can identify the slope once again by the variable m. But we're given a point on the line. And that point is given by the coordinates then x1 and y1. So what is that in our example?
Well, we can see that we have an x-coordinate of 3 and a y-coordinate of 6. So we can go ahead then and locate that on our graph. So x equals 1, 2, 3. And y equals 1, 2, 3, 4, 5, 6. There is a point that is on our line. So once again, we can start from this point and then interpret the slope to find other points on our line.
So I'm starting here. And our slope is negative 2. So that means that there is a rise of negative 2 and then a run of 1. So I'm going to go down 2 and over 1, down 2 and over 1, down 2 and over 1. So this then is the line for y minus 6 equals negative 2 times x minus 3.
Our last example is an equation given in standard form. So we want to graph the line 3x minus 5y equals 15. Now, the power to standard form is that we can pretty easily calculate x and y-intercepts. So remember, the x-intercept occurs at y equals 0. And the y-intercept occurs at x equals 0.
Now, what this means then is looking at our equation in standard form, if y equals 0, we can determine the x-intercept by solving simply for ax equals c. And if x equals 0, then we can find the y-intercept by solving for by equals c.
So let's go ahead then and calculate then the x-intercept. So this would be 3x equals 15 because y is 0. So this sort of disappears. So solving for x, we see that x equals 5. So let's locate x equals 5. And we know this is when y equals 0.
For the y-intercept, we can write this as negative 5y equals 15 because this would be 0. x equals 0. So we'd just have negative 5y equals 15. Well, dividing both sides by negative 5, we see that y equals negative 3. So let's locate that on our graph. y equals negative 3. And of course, x equals 0.
So now, we have two points on our line. They both happen to be intercepts. And that's all we need when graphing a line, just two points. So let's connect the dots and extend them to infinity. And there is the line for 3x minus 5y equals 15.
So let's review graphing linear equations. We looked at an equation in slope-intercept form, y equals mx plus b. We can identify the slope and the y-intercept from this form. We looked at point-slope form. This is y minus y1 equals m times x minus x1. And you can look at the point x1, y1, and then interpret that slope rise over run to look at other points on the line.
And we looked at standard form-- ax plus by equals c. And this allowed us to easily calculate the x-intercept and the y-intercept, giving us two points, which is all we need to connect the dots and graph a line. So thanks for watching this tutorial on graphing linear equations. Hope to see you next time.