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Hi, I'm a banana, and today we're going to learn about x and y intercepts.
Now, x-intercepts are any points that end up on the x-axis.
y-intercepts are any points that end up on the y-axis.
So let's actually find the coordinates of each of these green points, the x-intercepts.
This one right here...let's see, -1, -2, -3, -4...this it (-4,0).
This piont right here is (2,0).
3, 4...this point here is (5,0).
And this last point is (7,0).
Now, other than all being x-intercepts, do you notice anything else they all have in common?
You may notice that all of them have 0 as the y-coordinate.
Uhh...this one right here has the coordinates (0,-1).
Now, let's look at the y-intercepts, these red dots.
This one down here...let's see -2, -3, -4, -5...so (0,-5).
Up here, (0,4) and (0,6).
You may notice all the y-intercepts have 0's as their x-coordinates.
And that's going to be helpful in finding x and y-intercepts when we don't have a graph to work with.
Let's look at that.
Here, we have to find the x and y intercepts of the line: 3x - 4y = 12.
So, there's going to be a line that crosses the x and y axis, and our job is to figure out exactly where does it cross.
In other words, what is the x-intercept? What is the y-intercept?
Now, in order to be an x-intercept, the y-coordinate has to be 0.
So what we can do here is actually plug in a 0 for y and solve for x.
Let's try that.
So 3x - 4...and instead of writing y, I'm going to put a 0 there...equals 12.
So, 4 times 0 is just 0, so we end up with 3x = 12.
And x = 4.
That means our x-intercept is at (4,0).
Now, let's find the y-intercept.
To find the y-intercept, we're going to plug in a 0 for x.
So we have 3 times 0 minus 4y equals 12.
And we end up with -4y = 12.
Divide both sides by -4.
And we get y = -3.
So our y-intercept is at (0,-3).
Now, using our x-intercept and our y-intercept, we can actually quickly graph this line.
We just need to graph the point (4,0) and the point (0,-3).
So (4,0), our x-intercept, is right here.
And (0,-3), our y-intercept, is right here.
All we have to do is connect those points...
And there's a graph of our line.
Now, if you're used to using x,y tables, there's one more way we can calculate the x and y intercepts.
When you make an x,y table...
...you simply need to find out what's the value of x when y equals 0 (that will tell you the x-intercept), and what's the value of y when x equals 0 (that will tell you the x-intercept) -- or the y-intercept, sorry.
Alright, good luck!