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1. Sketch the graph of 3x + 2y = 6.
If x = 0, then y = 3
The y-intercept is (0, 3)
If y = 0, then x = 2
The x-intercept is (2, 0)
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2. Sketch the graph of x - 2y = 4.
If x = 0, then y = -2
The y-intercept is (0, -2)
If y = 0, then x = 4
The x-intercept is (4, 0)
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7. Sketch the graph of 3x + 2y < 6.
The boundary line is the line whose graph was produced in Example 1 at the left.
The origin is not on the boundary line so use it as the test point.
Testing (0, 0) produces 3(0) +2(0) < 6
which is TRUE.
Therefore the solution set is the half-plane
containing the origin and bounded by the line 3x + 2y = 6.
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3. Sketch the graph of 3x + 5y = 5.
If x = 0, then y = 1
The y-intercept is (0, 1)
If y = 0, then x = 5/3
The x-intercept is (5/3, 0)
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4. Sketch the graph of 3x + 2y = 0.
If x = 0, then y = 0
The y-intercept is (0, 0).
The x and y intercepts are the same so we must determine another point.
Substitute any value for x and solve for y or substitue any value for y and solve for x.
If x = 2, then y = -3
Plot the point (2, -3) and draw the line through
(2, -3) and (0, 0).
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8. Sketch the graph of 3x + 2y < 0.
The boundary line is the line whose graph was produced in Example 4 at the left.
The origin is on the boundary line so we must use another test point.
Pick (1, 1) as the test point because it is not on the boundary line and
the substitutions will be easy.
Testing (1, 1) produces 3(1) +2(1) < 0
which is FALSE.
Therefore the solution set is the half-plane
NOT containing (1, 1) and bounded by the line
3x + 2y = 0.
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5. Sketch the graph of y = 3x - 9.
If x = 0, then y = -9
The y-intercept is (0, -9)
If y = 0, then x = 3
The x-intercept is (3, 0)
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6. Sketch the graph of 5x = 10 - 2y.
If x = 0, then y = 5
The y-intercept is (0, 5)
If y = 0, then x = 5
The x-intercept is (5, 0)
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9. Sketch the graph of -3x + y ≤ 9.
The boundary line is the graph of -3x + y = 9.
If x = 0, then y = 9.
Therefore (0, 9) is the y-intercept
If y = 0, then x = -3.
Therefore (-3, 0) is the x-intercept.
The origin is not on the boundary line so use it as the test point.
Testing (0, 0) produces -3(0) + (0) ≤ 9
which is TRUE.
Therefore the solution set is the half-plane
containing the origin and bounded by the line -3x + y = 9..
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