Graph Using Intercepts - 2012 Book Archive

Definition of x- and y-Intercepts

The x-interceptThe point (or points) where a graph intersects the x-axis, expressed as an ordered pair (x, 0). is the point where the graph of a line intersects the x-axis. The y-interceptThe point (or points) where a graph intersects the y-axis, expressed as an ordered pair (0, y). is the point where the graph of a line intersects the y-axis. These points have the form (x, 0) and (0, y), respectively.

To find the x- and y-intercepts algebraically, use the fact that all x-intercepts have a y-value of zero and all y-intercepts have an x-value of zero. To find the y-intercept, set x=0 and determine the corresponding y-value. Similarly, to find the x-intercept, set y=0 and determine the corresponding x-value.

 

Example 1: Find the x- and y-intercepts: −3x+2y=12.

Solution: To find the x-intercept, set y = 0.

Therefore, the x-intercept is (−4, 0). To find the y-intercept, set x = 0.

Hence the y-intercept is (0, 6). Note that this linear equation is graphed above.

Answer: x-intercept: (−4, 0); y-intercept: (0, 6)

 

Example 2: Find the x- and y-intercepts: y=−3x+9.

Solution: Begin by finding the x-intercept.

The x-intercept is (3, 0). Next, determine the y-intercept.

The y-intercept is (0, 9).

Answer: x-intercept: (3, 0); y-intercept: (0, 9)

 

Keep in mind that the intercepts are ordered pairs and not numbers. In other words, the x-intercept is not x=2 but rather (2, 0). In addition, not all graphs necessarily have both intercepts: for example,

The horizontal line graphed above has a y-intercept of (0, −2) and no x-intercept.

The vertical line graphed above has an x-intercept (3, 0) and no y-intercept.

 

Try this! Find the x- and y-intercepts: 4x−y=2.

Answer: x-intercept: (1/2, 0); y-intercept: (0, −2)

Video Solution

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