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| PAGE: 110 | SET: Exercises | PROBLEM: 46 |
The graph of the inequality 
is the shaded region and boundary of the inequality is
. To graph the boundary, find the x-intercept and y-intercept of the line.
First find the y-intercept.
The y-intercept is the value of y, when 
.
(Substitute 
)
(Multiply: 
)
(Apply Additive identity property: 
)
The y-intercept is – 5, so the graph intersects the y-axis at (0, – 5).
Next find the x-intercept.
The x-intercept is the value of x, when 
.
(Substitute 
)
(Add 5 to each side)
(Simplify)
(Divide each side by 3)
(Cancel common terms)
(Divide: 
)
The x-intercept is 1.66, so the graph intersects the x-axis at (1.66, 0).
To draw inequality follow the steps.
1. Draw a coordinate plane.
2. Plot the points.
3. Since inequality symbol is 
, the boundary is included in the solution set. Graph the boundary of the inequality with a solid line.
4. To determine which half-plane to be shaded use a test point in either half-plane. A simple choice is (0, 0).
Substitute and y = 0 in original inequality .
The statement is false.
4. Since the statement is false, shade the region that do not contains point (0, 0).
Inequality graph is
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