Graphing Lines by Slope-Intercept Method

Summary of Graphing Lines

1. Plotting points by making a table of ordered pairs always works, but can be time-consuming.
   
2. Finding the x-intercept and y-intercept doesn’t work if it goes through the origin.
   
3. Slope-intercept method works unless it is a vertical line (x = k).
   

How to graph lines using the Slope-Intercept Method?

1. Solve the equation for y to put in the form y = mx + b.
   
2. Identify slope (m) and the y-intercept (0,b).
   
3. Plot the y-intercept (0,b).
   
4. Starting from (0,b), use the slope to find more points.
   
5. Draw a line through all the points.
   

The following diagrams show how to graph a line using the slope-intercept method. Scroll down the page for more examples and solutions.

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

Slope-intercept form of a line, and how to identify the slope and y-intercept from an equation
Examples:
Graph
a) y = 3x - 1
b) 2x + 5y = 10
c) 4x - 5y = 15

• Show Step-by-step Solutions

How to graph a line using the slope-intercept method? Given the equation y = mx + b

1. Plot the point (0,b)
   
2. Use slope to find more points.
   Examples:
   a) Graph y = 2x - 3
   b) Graph y = -2/3 x + 1
   c) Graph y = -4x
   d) Graph y = -2

• Show Step-by-step Solutions

Graphing Lines using the slope intercept method
Examples:
a) Graph 2x - 3y = 6
b) Graph 5x - 3y = 9
c) Graph x = -1
Since there is no y-term, we can’t put the equation in slope-intercept form and we can’t use the slope-intercept method.
Any line in the form x = k is a vertical line with x-intercept k.
d) Graph y = 1

• Show Step-by-step Solutions

This is a summary of the 3 methods for graphing lines: plotting points, x-intercept and y-intercept, slope intercept method.
Examples:
Graph
a) y = 3x - 1
b) 2x + 5y = 10
c) 4x - 5y = 15

• Show Step-by-step Solutions

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