To graph the inequality + ≤ , we will start by finding the boundary line.
The boundary line is the line that results from changing the inequality to an equation. To find the equation of the line, we will solve for :
+ ≤
≤ − +
≤ −/ +
So, the equation of the boundary line is = −/ + .
Next, we will determine which side of the line to shade. Since the inequality is less than or equal to, we will shade the region below the line. This region is the solution set for the inequality.
The graph of the inequality is shown below:
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| x + 3y <= 6
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The shaded region is below the line. To test a point in the region, we can pick any point in the shaded region, such as (0, 2), and substitute its coordinates into the inequality:
(0) + (2) ≤
6 ≤ 6
The inequality is true, so the solution set includes the point (0, 2).
Thus, the solution set for the inequality + ≤ is the shaded region below the line = −/ + , including the boundary line itself.
Answers & Comments
Answer:
To graph the inequality + ≤ , we will start by finding the boundary line.
The boundary line is the line that results from changing the inequality to an equation. To find the equation of the line, we will solve for :
+ ≤
≤ − +
≤ −/ +
So, the equation of the boundary line is = −/ + .
Next, we will determine which side of the line to shade. Since the inequality is less than or equal to, we will shade the region below the line. This region is the solution set for the inequality.
The graph of the inequality is shown below:
|
|
| x + 3y <= 6
|
|
----------|----------
|
|
|
The shaded region is below the line. To test a point in the region, we can pick any point in the shaded region, such as (0, 2), and substitute its coordinates into the inequality:
(0) + (2) ≤
6 ≤ 6
The inequality is true, so the solution set includes the point (0, 2).
Thus, the solution set for the inequality + ≤ is the shaded region below the line = −/ + , including the boundary line itself.