Graphing Lines by Slope-Intercept

The Slope-Intercept Equation
The equation y = mx + b is called the slope-intercept form of a line.
The equation represents a line where m = slope and b = y-intercept (0, b)

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

How to graph the equation?
The slope-intercept form of a linear equation is:
y = mx + b
where:
m = slope (steepness and direction of the line)
b = y-intercept (where the line crosses the y-axis)

1. Identify the Slope (m) and Y-Intercept (b)
   Given an equation like:
   y = 2x − 3
   Slope (m) = 2
   Y-intercept (b) = -3
   

2. Plot the Y-Intercept
   Start at the y-intercept (0,b) on the y-axis.
   For y = 2x − 3, plot the point (0,−3).
   

3. Use the Slope to Find a Second Point
   Slope = Rise/Run
   Rise = Vertical change (up/down)
   Run = Horizontal change (left/right)
   For m = 2 = 2/1
   From (0,−3), move up 2 units (rise = +2).
   Move right 1 unit (run = +1).
   New point: (1,−1).
   Plot the point (1,-1)
   

4. Draw a line to connect the two points and extend the line in both directions.

How to graph a linear equation given in slope intercept form?
Examples:
Identify the slope and y-intercept. Graph.
a) y = -2/3 x + 1
b) y = 5x - 2
c) y = x
d) 3x - 2y = 8

• Show Step-by-step Solutions

How to graph a line in slope intercept form with a negative fractional slope and a negative y-intercept?
Example:
Graph using slope-intercept form
y = -2/3 x - 5

• Show Step-by-step Solutions

How to graph a line in slope intercept form with a negative integer slope and a positive integer y-intercept?
Example:
Graph using slope-intercept form
y = -2x + 5

• Show Step-by-step Solutions

How to graph a line in slope intercept form with a positive integer slope and a negative y-intercept?
Example:
Graph using slope-intercept form
y = 3x - 2

• Show Step-by-step Solutions

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