Graphing Lines by X and Y-Intercepts

Graphing a line using its x-intercept and y-intercept is a quick and accurate method, especially for equations in standard form (Ax + By = C).

The following diagrams show how to graph lines using the X and Y intercepts. Scroll down the page for more examples and solutions on graphing lines using x and y intercepts.

 

Coordinate Geometry Worksheets
Practice your skills with the following worksheets:
Printable & Online Coordinate Geometry Worksheets

1: Find and plot the x-intercept
The x-intercept is where the line crosses the x-axis.
How to find it:
Substitute y = 0 into the equation and solve for x.
Plot the x-intercept: (x,0).

2. Find and plot the y-intercept
The y-intercept is where the line crosses the y-axis
How to find it:
Substitute x = 0 into the equation and solve for
Plot the y-intercept: (0,y).

3. Draw the Line
Connect the two intercepts with a straight line.
Extend the line in both directions.

Example: Graph the line 2x + 3y = 6

1. Find the x-intercept:
   Set y = 0 in the equation:
   2x + 3(0) = 6, 2x + 0 = 6, 2x = 6 x = 3
   The x-intercept is the point (3, 0).

2. Find the y-intercept:
   Set x = 0 in the equation: 2(0) + 3y = 6, 0 + 3y = 6, 3y = 6, y = 2
   The y-intercept is the point (0, 2).
   

3. Plot the intercepts:
   On your coordinate plane, plot the point (3, 0).
   Plot the point (0, 2).
   Draw a line that passes through the points (3, 0) and (0, 2).
   

Special Cases:
Horizontal Lines: Equations of the form y = c (where ‘c’ is a constant) are horizontal lines passing through the point (0, c).
Vertical Lines: Equations of the form x = c (where ‘c’ is a constant) are vertical lines passing through the point (c, 0).
Line Passing Through the Origin: If the equation has no constant term (e.g., y = 2x), both the x and y intercepts will be (0, 0). In this case, you’ll need to find another point by substituting a non-zero value for x (or y) to graph the line.

How to Graph Lines Using X, Y Intercepts?

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