How to Graph Linear Equations Using the Intercepts Method

The intercepts method of graphing a line uses the two intercepts of a line to determine its equation. It is different from the slope-intercept method, but similar. Since it means knowing the two points where the line intercepts the x- and y-axis, the graphing approach is the same as if you start off knowing just two points.

Instructions

1. Convert the two intercepts into point coordinates.

   For example, if you are given that the x-intercept is 2 and the y-intercept is -4, then the intercept points are (x,y)=(2,0) and (x,y)=(0,-4).

2. Graph by drawing a line straight through these two points.

3. 

   Alternatively, make an equation of these two points.

   The slope of the line is the rise over run between the two points: "y/"x. (Note that " means "difference between two numbers.") For our example, the slope is (0--4)/(2-0) = 2.

4. 

   Insert the slope and the y-intercept into the slope-intercept form.

   For slope m and y-intercept b, the equation is y=mx+b. For our example, that's y=2x-4.

5. Check your work.

   Make sure the points upon which the equation are based do actually solve the equation. For example, (0,-4) does solve it, because (-4)=2---(0)-4.

6. Plot some points using the equation.

   Insert x-values to find the corresponding y-values. Then plot these (x,y) points.

7. 

   Draw the full line out by drawing through the plotted points.

   As few as two points are needed to do so.

Tips & Warnings

• What if there is only one intercept? That means the line is either horizontal or vertical. If the intercept is an x-intercept, then just draw a vertical line through it. If the intercept is a y-intercept, then just draw a horizontal line through the y-intercept (see last diagram above). In this case, only one point is needed to draw the full line.

References

• Intercepts Method For Graphing Functions