Another method to graph a line in the XY-plane is to use the intercepts. What are intercepts? These are points of the line that are found on the \color{red}\large{x} and \color{red}\large{y} axes. There are two kinds of intercepts.
Here is a quick diagram that gives you the idea.
Since the x-intercept is a point where the line crosses the x-axis, it is a point with a y-value of zero.
In the same manner, since the y-intercept is a point where the line crosses the y-axis, it must be a point with an x-value of zero.
Using the informal definitions of x and y-intercepts above, it makes a lot of sense why the procedures below on how to find them work! Rules on How to Find the InterceptsLet y = 0 in the equation, then solve for x. Let x = 0 in the equation, then solve for y. Examples of How to Graph a Line using the x and y-interceptsExample 1: Graph the equation of the line 2x-4y=8 using its intercepts. I hope you recognize that this is an equation of a line in Standard Form where both the x and y variables are found on one side of the equation opposite the constant term. It is a common practice in an algebra class to ask students to graph the line using the intercept method when the line is in Standard Form. Here we go! Let y=0 in the equation, then solve for x.
The x-intercept is (4, 0). Let x=0 in the equation, then solve for y.
The y-intercept is (0, –2). Now we can plot the two points on the xy axis and connect them using a straight edge ruler to show the graph of the line.
Example 2: Graph the equation of the line using its intercepts.
This equation of the line is in the Slope-Intercept Form. We can actually graph this using another technique which uses the slope and the y-intercept taken directly from the equation. You can see a separate tutorial here. Since this lesson is about intercepts, let’s work this out using this method. Let y=0 in the equation, then solve for x.
The x-intercept is (–2, 0). Let x=0 in the equation, then solve for y.
The y-intercept is (0, 3). Plot the intercepts in the axes and draw a straight line passing through them using a ruler.
You might also be interested in: Three Ways to Graph a Line
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