Graphing Linear Functions

Graph a linear function: a step by step tutorial with examples and detailed solutions. Free graph paper is available.

Linear Functions: Any function of the form f (x) = m x + b, where m is not equal to 0 is called a linear function. The domain of this function is the set of all real numbers. The range of f is the set of all real numbers. The graph of f is a line with slope m and y intercept b.
Note: A function f (x) = b, where b is a constant real number is called a constant function. Its graph is a horizontal line at y = b.


Example 1: Graph the linear function f given by

f (x) = 2x + 4

Solution to Example 1

  • You need only two points to graph a linear function. These points may be chosen as the x and y intercepts of the graph for example.
  • Determine the x intercept, set f(x) = 0 and solve for x.

      2x + 4 = 0

      x = -2


  • Determine the y intercept, set x = 0 to find f(0).

      f(0) = 4


  • The graph of the above function is a line passing through the points (-2 , 0) and (0 , 4) as shown below.

    graph of f(x)=2x + 4

Matched Problem : Graph the linear function f given by

f (x) = x + 3



Example 2: Graph the linear function f given by

f (x) = -(1 / 3)x - 1 / 2

Solution to Example 2

  • Determine the x intercept, set f(x) = 0 and solve for x.

      -(1 / 3)x - 1 / 2 = 0

      x = - 3 / 2


  • Determine the y intercept, set x = 0 to find f(0).
      f(0) = -1 / 2

  • The graph of the above function is a line passing through the points (-3 / 2 , 0) and (0 , -1 / 2) as shown below.

  • graph of f(x)=-(3 / 2x - 1 / 2

Matched Problem : Graph the linear function f given by

f (x) = -x / 5 + 1 / 3

More references and links to graphing and graphs of functions.


Graphing Functions


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Updated: 2 April 2013

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