*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.

**Instructional Video**: Graphing by Finding Intercepts

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**The answer is NO. Horizontal lines, of the form

*x*- and*y*-intercepts?*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**: