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.

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

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

The graph of the above function is a line passing through
the points (3 / 2 , 0) and (0 , 1 / 2) as shown below.
Matched Problem : Graph the linear function f given by
f (x) = x / 5 + 1 / 3
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Updated: February 2015
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