You might be familiar with the basic fact that two points determine a line. This fact leads to a nice and easy way to graph lines using the two points called the

*x*- and

*y*-intercepts.

All

*x*-intercepts, if they exist, must have a corresponding

*y*-value of zero. All

*y*-intercepts must have a corresponding

*x*-value of zero. This might sound confusing but just remember the following steps to algebraically find intercepts.

**Example**: Graph 3

*x* − 5

*y* = 15 using the

*x*- and

*y*-intercepts.

Plot the points and draw a line through them with a straight edge.

This is a nice and easy method for determining the two points you need for graphing a line. In fact, we will use this exact technique for finding intercepts when we study the graphs of all the conic sections later in our study of Algebra. Be careful not to say that

*y* = −3 is the

*y*-intercept because the intercepts, actually, are ordered pairs or points on the graph so you should take care to say (0,−3) is the

*y*-intercept.

**Use the given graph to answer the question.**
Be sure to pay attention to the scale. Misreading the scale is the most common error in this type of problem.

**Example**: Graph −4

*x* + 3

*y* = 12 using the intercepts.

**Example**: Graph −4

*x* + 2

*y* = −6 using the intercepts.

**Example**: Graph

*y* = −5

*x* +15 using the intercepts.

**Example**: Graph

*y* = −3/4

*x* + 9 using the intercepts.

This brings us to one of the most popular questions in linear graphing.

**Do all lines have ***x*- and *y*-intercepts? The answer is NO. Horizontal lines, of the form

*y* =

*b*, do not necessarily have

*x*-intercepts. Vertical lines, of the form

*x* =

*a*, do not necessarily have

*y*-intercepts.

**Example**: Graph

*y* = 3.

**Example**: Graph

* x* = −2.

**Video Examples on YouTube**: