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?

• Show Step-by-step Solutions

Graphing Linear Functions by Finding X,Y Intercept

• Show Step-by-step Solutions

Intercepts and graphing linear equations

• Show Step-by-step Solutions

Check out our most popular games!
Fraction Concoction	Fact Family Game	Number Bond Garden
Online Addition Subtraction Game	Penguin Solitaire	Sawayama Solitaire
Ark Solitaire	Eldritch Invasion	Shenzhen Solitaire

Check out more Solitaire games here.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.