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Sagot :
Certainly! Let's go step by step to match each ordered pair with the appropriate equation.
Given equations are:
1. [tex]\( y = 3x - 4 \)[/tex]
2. [tex]\( y = \frac{1}{2}x + 2 \)[/tex]
And the ordered pairs are:
- [tex]\( (3,5) \)[/tex]
- [tex]\( (4,4) \)[/tex]
- [tex]\( (5,11) \)[/tex]
- [tex]\( (6,14) \)[/tex]
- [tex]\( (2,3) \)[/tex]
### Matching [tex]\( (3,5) \)[/tex]
1. For equation [tex]\( y = 3x - 4 \)[/tex]:
[tex]\[ y = 3(3) - 4 = 9 - 4 = 5 \][/tex]
This matches the y-value of 5.
2. For equation [tex]\( y = \frac{1}{2}x + 2 \)[/tex]:
[tex]\[ y = \frac{1}{2}(3) + 2 = 1.5 + 2 = 3.5 \][/tex]
This does not match the y-value of 5.
Thus, [tex]\( (3,5) \)[/tex] matches with [tex]\( y = 3x - 4 \)[/tex].
### Matching [tex]\( (4,4) \)[/tex]
1. For equation [tex]\( y = 3x - 4 \)[/tex]:
[tex]\[ y = 3(4) - 4 = 12 - 4 = 8 \][/tex]
This does not match the y-value of 4.
2. For equation [tex]\( y = \frac{1}{2}x + 2 \)[/tex]:
[tex]\[ y = \frac{1}{2}(4) + 2 = 2 + 2 = 4 \][/tex]
This matches the y-value of 4.
Thus, [tex]\( (4,4) \)[/tex] matches with [tex]\( y = \frac{1}{2}x + 2 \)[/tex].
### Matching [tex]\( (5,11) \)[/tex]
1. For equation [tex]\( y = 3x - 4 \)[/tex]:
[tex]\[ y = 3(5) - 4 = 15 - 4 = 11 \][/tex]
This matches the y-value of 11.
2. For equation [tex]\( y = \frac{1}{2}x + 2 \)[/tex]:
[tex]\[ y = \frac{1}{2}(5) + 2 = 2.5 + 2 = 4.5 \][/tex]
This does not match the y-value of 11.
Thus, [tex]\( (5,11) \)[/tex] matches with [tex]\( y = 3x - 4 \)[/tex].
### Matching [tex]\( (6,14) \)[/tex]
1. For equation [tex]\( y = 3x - 4 \)[/tex]:
[tex]\[ y = 3(6) - 4 = 18 - 4 = 14 \][/tex]
This matches the y-value of 14.
2. For equation [tex]\( y = \frac{1}{2}x + 2 \)[/tex]:
[tex]\[ y = \frac{1}{2}(6) + 2 = 3 + 2 = 5 \][/tex]
This does not match the y-value of 14.
Thus, [tex]\( (6,14) \)[/tex] matches with [tex]\( y = 3x - 4 \)[/tex].
### Matching [tex]\( (2,3) \)[/tex]
1. For equation [tex]\( y = 3x - 4 \)[/tex]:
[tex]\[ y = 3(2) - 4 = 6 - 4 = 2 \][/tex]
This does not match the y-value of 3.
2. For equation [tex]\( y = \frac{1}{2}x + 2 \)[/tex]:
[tex]\[ y = \frac{1}{2}(2) + 2 = 1 + 2 = 3 \][/tex]
This matches the y-value of 3.
Thus, [tex]\( (2,3) \)[/tex] matches with [tex]\( y = \frac{1}{2}x + 2 \)[/tex].
### Summary of Matches:
- [tex]\( y = 3x - 4 \)[/tex]: [tex]\( (3,5) \)[/tex], [tex]\( (5,11) \)[/tex], [tex]\( (6,14) \)[/tex]
- [tex]\( y = \frac{1}{2}x + 2 \)[/tex]: [tex]\( (4,4) \)[/tex], [tex]\( (2,3) \)[/tex]
Given equations are:
1. [tex]\( y = 3x - 4 \)[/tex]
2. [tex]\( y = \frac{1}{2}x + 2 \)[/tex]
And the ordered pairs are:
- [tex]\( (3,5) \)[/tex]
- [tex]\( (4,4) \)[/tex]
- [tex]\( (5,11) \)[/tex]
- [tex]\( (6,14) \)[/tex]
- [tex]\( (2,3) \)[/tex]
### Matching [tex]\( (3,5) \)[/tex]
1. For equation [tex]\( y = 3x - 4 \)[/tex]:
[tex]\[ y = 3(3) - 4 = 9 - 4 = 5 \][/tex]
This matches the y-value of 5.
2. For equation [tex]\( y = \frac{1}{2}x + 2 \)[/tex]:
[tex]\[ y = \frac{1}{2}(3) + 2 = 1.5 + 2 = 3.5 \][/tex]
This does not match the y-value of 5.
Thus, [tex]\( (3,5) \)[/tex] matches with [tex]\( y = 3x - 4 \)[/tex].
### Matching [tex]\( (4,4) \)[/tex]
1. For equation [tex]\( y = 3x - 4 \)[/tex]:
[tex]\[ y = 3(4) - 4 = 12 - 4 = 8 \][/tex]
This does not match the y-value of 4.
2. For equation [tex]\( y = \frac{1}{2}x + 2 \)[/tex]:
[tex]\[ y = \frac{1}{2}(4) + 2 = 2 + 2 = 4 \][/tex]
This matches the y-value of 4.
Thus, [tex]\( (4,4) \)[/tex] matches with [tex]\( y = \frac{1}{2}x + 2 \)[/tex].
### Matching [tex]\( (5,11) \)[/tex]
1. For equation [tex]\( y = 3x - 4 \)[/tex]:
[tex]\[ y = 3(5) - 4 = 15 - 4 = 11 \][/tex]
This matches the y-value of 11.
2. For equation [tex]\( y = \frac{1}{2}x + 2 \)[/tex]:
[tex]\[ y = \frac{1}{2}(5) + 2 = 2.5 + 2 = 4.5 \][/tex]
This does not match the y-value of 11.
Thus, [tex]\( (5,11) \)[/tex] matches with [tex]\( y = 3x - 4 \)[/tex].
### Matching [tex]\( (6,14) \)[/tex]
1. For equation [tex]\( y = 3x - 4 \)[/tex]:
[tex]\[ y = 3(6) - 4 = 18 - 4 = 14 \][/tex]
This matches the y-value of 14.
2. For equation [tex]\( y = \frac{1}{2}x + 2 \)[/tex]:
[tex]\[ y = \frac{1}{2}(6) + 2 = 3 + 2 = 5 \][/tex]
This does not match the y-value of 14.
Thus, [tex]\( (6,14) \)[/tex] matches with [tex]\( y = 3x - 4 \)[/tex].
### Matching [tex]\( (2,3) \)[/tex]
1. For equation [tex]\( y = 3x - 4 \)[/tex]:
[tex]\[ y = 3(2) - 4 = 6 - 4 = 2 \][/tex]
This does not match the y-value of 3.
2. For equation [tex]\( y = \frac{1}{2}x + 2 \)[/tex]:
[tex]\[ y = \frac{1}{2}(2) + 2 = 1 + 2 = 3 \][/tex]
This matches the y-value of 3.
Thus, [tex]\( (2,3) \)[/tex] matches with [tex]\( y = \frac{1}{2}x + 2 \)[/tex].
### Summary of Matches:
- [tex]\( y = 3x - 4 \)[/tex]: [tex]\( (3,5) \)[/tex], [tex]\( (5,11) \)[/tex], [tex]\( (6,14) \)[/tex]
- [tex]\( y = \frac{1}{2}x + 2 \)[/tex]: [tex]\( (4,4) \)[/tex], [tex]\( (2,3) \)[/tex]
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