Graphing lines can be done in a number of ways. This section describes a method, plotting points, that always works and can be used for many other types of equations. Notice that in a linear equation with two variables,

*y* = 3

*x* - 2, the

*y*-value depends on what the

*x*-value is. Since

*x* is independent here, choose any real number, say

*x* = 4, and you can find the corresponding

*y*-value by evaluating y = 3(4) – 2 = 12 – 2 = 10. Therefore, the ordered pair (4, 10) is a point on the graph of the equation.

**Example**: Graph

*y* = −2

*x* + 6 by plotting five points.

**Step 1**: Choose any five

*x*-values.

**Step 2**: Evaluate to find the corresponding

*y*-values.

**Step 3:** Plot the points and use a straight edge to draw a line through them.

When choosing

*x*-values it is wise to pick some negative numbers as well as zero. Try to find the points where the line crosses the

*x* and

*y* axes. These special points are called the

*x*- and

*y*-intercepts.

**Is the given point a solution?**
Remember that we are less likely to make a mistake if we insert parentheses where we see a variable and then substitute in the appropriate values.

**Find the corresponding value.**
**Graph by plotting points**.

**Example**: Graph

*y* = 2

*x* − 4 by plotting five points.

**Example:** Graph

*y* = −

*x *− 2 by plotting five points.

Choosing a scale when creating a blank coordinate system will take some thought. Keep in mind that the scale on the

*x*-axis need not be the same as the scale on the

*y*-axis.

**Example**: Graph

*y* = 1/2

*x* − 6 by plotting five points.

When the coefficient of

*x* is a fraction, choose

*x*-values to be multiples of the denominator so that you might avoid unnecessarily tedious calculations.

**Example**: Graph

*y* = −3/2

*x* + 6 by plotting five points.

**Example**: Graph 2

*x *− 3

*y* = 6 by plotting five points.

When dividing a binomial by a number you must

*divide both terms* by that number. For example, treat the −3 as a common denominator as in the previous problem.

A common error is to just divide the 6 by −3.

**Video Examples on YouTube**: