This document provides an explanation and examples of using intercepts to graph linear equations. It defines x-intercept as the x-coordinate where the graph crosses the x-axis and y-intercept as the y-coordinate where the graph crosses the y-axis. Examples are given of finding intercepts of equations by setting either x or y to 0 and then solving for the other variable. The intercepts are then used to graph the line.

1. Lesson: Graphing
Using Intercepts
Courtesy of BSN

2. x-intercept – x-coordinate of a point where the graph crosses the x-
axis.
y-intercept – y-coordinate of a point where the graph crosses the y-
axis.
y-intercept
(0, 2)
x-intercept
(4, 0)

3. EX Find the x-intercept and the y-intercept of the graph of 2x + 3y = 12.
y-intercept x-intercept
Let x = 0. Let y = 0.
2 x 3 y 12 2 x 3 y 12
2(0) 3 y 12 2x 3(0) 12
3y 12 2x 12
3 3 2 2
y 4 x 6
(0, 4) (6, 0)

4. EX Graph the equation 3x + 5y = 15 using intercepts.
y-intercept x-intercept
Let x = 0. Let y = 0.
3x 5 y 15 3x 5 y 15
3(0) 5 y 15 3x 5(0) 15
5y 15 3x 15
5 5 3 3
y 3 x 5
•
•

5. EX You are helping to plan a dinner at your school and you need to
rent tables to seat 144 people. Small tables seat 6 people and large
tables seat 8 people.
6x + 8y = 144 x = number of small tables
y = number of large tables
a. Find the intercepts and graph the equation.
b. Give four possibilities for the numbers of each size table.
y-intercept x-intercept
Let x = 0. Let y = 0.
6 x 8 y 144 6 x 8 y 144
6(0) 8 y 144 6x 8(0) 144
8y 144 6x 144
8 8 6 6
y 18 x 24 •
0 small and 18 large
24 small and 0 large
•
8 small and 12 large
16 small and 6 large