You've learned one way to graph a standard form equation - by converting it to slope intercept form. Click here to review this lesson.
There is another way to graph standard form equations, and that is to find the x and y intercepts.
Now let's review what the term intercepts means. An intercept is where your line crosses an axis. We have an x intercept and a y intercept.
The point where the line touches the x axis is called the x intercept. The point where the line touches the y axis is called the y intercept.
Take a look at the graph below.
If we can find the points where the line crosses the x and y axis, then we would have two points and we'd be able to draw a line.
When equations are written in standard form, it is pretty easy to find the intercepts. Take a look at this diagram, as it will help you to understand the process.
Now, let's apply this. Just remember:
This concept can be confusing, so let's take a look at the video to explain the first example.
Ok.. now let's look at a real world problem that we can solve using intercepts.
Emily received a gift card for her birthday and decided to download a few books. She downloaded a few $6 books and a few $3 books. She spent $30 on books. The equation that represents x number of $6 books and y number of $3 books is:
6x + 3y = 30
The x-intercept is (5,0). The x-intercept means that if no $3 books are purchased, Emily could purchase 5, $6 books for $30.
By reading our graph, we see that if Emily bought 3, $6 books, she could buy 4, $3 books.
Let's prove it!
6x + 3y = 30
6(3) + 3(4) = 30
18 + 12 = 30
30 = 30
It works! Therefore, (4,3) is a solution to this problem.
Great job on graphing equations.