Answer:
Explanation:
Let's complete the tables of values for each equation:
1. Equation: y = 2x - 4
x | 0 | 2 | 3
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y | -4 | 0 | 2
2. Equation: y = (1/2)x - 5
x | -5 | 4 | 6
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y | -7.5 | -3 | -2
3. Equation: y = (2/3)x + 4
x | -6 | -3 | 0
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y | -2 | 2 | 4
4. Equation: y = 2x - 8
x | 2 | 4 | 6
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y | -4 | 0 | 4
5. Equation: y = 4x - 12
x | 4 | 3 | 2
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y | 4 | 0 | -4
Now, let's find the equations represented by each line on the graph:
6. A: The line passing through points (2, 0) and (4, 4) represents the equation y = 2x - 4.
7. B: The line passing through points (-5, -7.5) and (6, -2) represents the equation y = (1/2)x - 5.
8. E: The line passing through points (-6, -2) and (0, 4) represents the equation y = (2/3)x + 4.
Now, let's find the y values that make each ordered pair a solution to the given equations:
9. 5x + y = 15
For (3, y):
5(3) + y = 15
15 + y = 15
y = 15 - 15
y = 0
For (4, y):
5(4) + y = 15
20 + y = 15
y = 15 - 20
y = -5
10. 2x + 3y = 6
For (6, y):
2(6) + 3y = 6
12 + 3y = 6
3y = 6 - 12
3y = -6
y = -6 / 3
y = -2
For (2, y):
2(2) + 3y = 6
4 + 3y = 6
3y = 6 - 4
3y = 2
y = 2 / 3
11. 6x - y = 0
For (0, y):
6(0) - y = 0
-y = 0
y = 0
For (1/2, y):
6(1/2) - y = 0
3 - y = 0
y = 3
12. 2x - 3y = 2
For (1, y):
2(1) - 3y = 2
2 - 3y = 2
-3y = 2 - 2
-3y = 0
y = 0
For (-1/2, y):
2(-1/2) - 3y = 2
-1 - 3y = 2
-3y = 2 + 1
-3y = 3
y = 3 / -3
y = -1
13. 7x + 3y = -4
For (-4, y):
7(-4) + 3y = -4
-28 + 3y = -4
3y = -4 + 28
3y = 24
y = 24 / 3
y = 8
For (2, y):
7(2) + 3y = -4
14 + 3y = -4
3y = -4 - 14
3y = -18
y = -18 / 3
y = -6
The y values that make each ordered pair a solution to the equations are as follows:
9. (3, 0), (4, -5)
10. (6, -2), (2, 2/3)
11. (0, 0), (1/2, 3)
12. (1, 0), (-1/2, -1)
13. (-4, 8), (2, -6)