To graph an inequality, we first graph the corresponding __________. So to graph the inequality y ≤ x + 1, we first graph the equation __________. To decide which side of the graph of the equation is the graph of the inequality, we use __________ points. Complete the table, and sketch a graph of the inequality by shading the appropriate region.
Test point | Inequality y ≤ x + 1 | Conclusion |
(0, 0) |
|
|
(0, 2) |
|
|
To evaluate: Steps to graph an inequality and draw the shaded portion of the graph of given inequality.
Explanation of Solution
Section1:
The graph of an inequality is basically the boundary of the graph of that equation without inequality symbol (> or <),
Therefore, replace the inequality sign with equal to sign and first graph the corresponding equation.
The corresponding equation is
To check which side of the corresponding equation is the graph of inequality put the test points in the equation.
Section2:
Given inequality equation is,
First graph the equation,
Substitute the different values of x and form a table for the corresponding value of y and join the points to plot the graph.
x | y |
0 | 1 |
1 | 2 |
2 | 3 |
To Graph the inequality,
Substitute 0 for x and 0 for y in the inequality,
Thus, the point (0, 0) satisfies the given equation.
Therefore, the shaded region of the graph is towards the origin.
Figure (1)
Figure (1) shows the graph of the inequality with shaded appropriate region.
Chapter 10 Solutions
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