To solve the inequality \( y \geq 3x \), we need to identify the points that satisfy this condition.
Step 1: Graph the equation
First, we'll graph the line represented by the equation \( y = 3x \). This is a straight line with a slope of 3 and a y-intercept at \( (0, 0) \).
Step 2: Determine the area for the inequality
Since this is a "greater than or equal to" inequality ( \( y \geq 3x \) ), the solution set includes all points on the line and all points above the line. The area above the line can be shaded to represent the solution set.
Step 3: Identify some coordinates
To identify some specific points that satisfy \( y \geq 3x \), we can pick several values for \( x \) and calculate the corresponding \( y \) values using the equation:
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Choose \( x = 0 \):
- \( y = 3(0) = 0 \)
- Point: \( (0, 0) \)
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Choose \( x = 1 \):
- \( y = 3(1) = 3 \)
- Point: \( (1, 3) \)
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Choose \( x = -1 \):
- \( y = 3(-1) = -3 \)
- Point: \( (-1, -3) \), but we need \( y \geq 3(-1) = -3 \), so this point is valid.
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Choose \( x = 2 \):
- \( y = 3(2) = 6 \)
- Point: \( (2, 6) \)
Step 4: Additional points
Here are some additional points that satisfy the inequality \( y \geq 3x \):
- For \( x = 2 \): \( (2, 6) \) (since \( 6 \geq 3(2) \))
- For \( x = -2 \): \( (-2, 0) \) (since \( 0 \geq 3(-2) = -6 \))
- For \( x = 0.5 \): \( (0.5, 2) \) (since \( 2 \geq 3(0.5) = 1.5 \))
Summary
The solution set for the inequality \( y \geq 3x \) includes the line \( y = 3x \) and the area above it. Some example coordinates that satisfy the inequality are:
- \( (0, 0) \)
- \( (1, 3) \)
- \( (2, 6) \)
- \( (-1, -3) \) (valid since it lies on the line)
- \( (-2, 0) \)
You can pick any point above the line for the inequality \( y \geq 3x \).
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