Teaching Notes 4.10: Using theX-Intercept and
theY-Intercept to Graph a Linear Equation
By finding thex-intercept and they-intercept, students can quickly graph a linear equation.
Typical errors result from not understanding the process for solving a linear equation and
graphing ordered pairs.SPECIAL MATERIALS:
Graph paper, rulers- Instruct your students to graph the equationx+ 2 y=6 in the coordinate plane by providing
the points (−4, 5), (4, 1), (−2, 4), (6, 0), (0, 3), and (8,−1). They should graph the points
and see that they lie on a line. - Because two points determine a line, students need to find only two solutions to a linear
equation in order to graph the equation. Two solutions that are easy to find are the
x−intercept and they-intercept. - Explain to your students that the points (6, 0) and (0, 3) in the example respectively repre-
sent thex-intercept and they-intercept. Thex-intercept is the point where the graph crosses
thex-axis. They-intercept is the point where the graph crosses they-axis. - Review the information and example on the worksheet with your students. Model how to
find these intercepts algebraically using the equationx+ 2 y=6. - Explain to your students that after they find the intercepts of the equation, they can use
these ordered pairs to create a graph. They should plot the two points and draw a line con-
necting them. This line represents the graph of the equation.
EXTRA HELP:
As a check, always select a third ordered pair that is a solution to the equation. If the ordered pair
is on the line, then the graph is correct.ANSWER KEY:
Thex-intercept is provided first and is followed by they-intercept. Use the intercepts to check
students’ graphs.(1)(4, 0); (0, 2) (2)(6, 0); (0, 2) (3)(−5, 0); (0, 10) (4)(3, 0); (0,−15)
(5)(9, 0); (0, 3) (6)(−5, 0); (0, 5) (7)(−6, 0); (0,−3) (8)(16, 0); (0, 2)
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(Challenge)Marcus is correct. Horizontal or vertical lines will have only one intercept.
------------------------------------------------------------------------------------------156 THE ALGEBRA TEACHER’S GUIDE