Student Help
STUDY TIP
The graph of
y > ax b is above
the graph of
y ax b. The
graph of y < ax b
is below the graph of
y ax b. Similar
rules apply for ≥ and ≤.
EXAMPLE
4
Use Slope-Intercept Form
Graph the inequality x y > 3 using the slope-intercept form of the
corresponding equation.
Solution
Write the corresponding equation in slope-intercept form.
xy3
Write corresponding equation.
y x 3
Subtract x from each side.
The graph of the line has a slope of 1 and a
y-intercept of 3. The inequality is >, so use a
dashed line.
y
xy>3
Test the origin: 0 0 0 and 0 is not greater
than 3, so (0, 0) is not a solution. Since (0, 0)
lies below the line, shade above the line.
ANSWER 䊳
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1
3
The graph of x y > 3 is all points
above the line. Check by testing any
point above the line.
EXAMPLE
5
1 (0, 0)
1
3
x
3
Use Slope-Intercept Form
Graph the inequality 2x y ≥ 2 using the slope-intercept form of the
corresponding equation.
Solution
Write the corresponding equation in slope-intercept form.
2x y 2
Write corresponding equation.
y 2x 2
Subtract 2x from each side.
y 2x 2
Multiply each side by 1.
The graph of the line has a slope of 2 and a
y-intercept of 2. The inequality is ≥, so use a
solid line.
Test the origin: 2(0) 0 0 and 0 is greater
than 2, so (0, 0) is a solution. Since (0, 0) lies
below the line, shade below the line.
ANSWER 䊳
The graph of 2x y ≥ 2 is all
points on and below the line. Check
by testing any point below the line.
y
3
3
1
2x y ≥ 2
(0, 0)
3
5 x
3
Use Slope-Intercept Form
Graph the inequality.
5. 2x y > 1
6. x y ≤ 4
6.8
7. 3x y ≤ 4
Graphing Linear Inequalities in Two Variables
369