For both equations below, [tex]$ x $[/tex] is the input and [tex]$ y $[/tex] is the output. Match the ordered pair with the correct equation by placing the ordered pair into the appropriate bin.

Equations:
[tex]\[ y = 3x - 4 \][/tex]
[tex]\[ y = \left(\frac{1}{2}\right)x + 2 \][/tex]

Ordered Pairs:
[tex]\[ (3, 5) \][/tex]
[tex]\[ (4, 4) \][/tex]
[tex]\[ (5, 11) \][/tex]
[tex]\[ (6, 14) \][/tex]
[tex]\[ (2, 3) \][/tex]

Question

06-08-2024
Mathematics

Answered

For both equations below, [tex]$ x $[/tex] is the input and [tex]$ y $[/tex] is the output. Match the ordered pair with the correct equation by placing the ordered pair into the appropriate bin.

Equations:
[tex]\[ y = 3x - 4 \][/tex]
[tex]\[ y = \left(\frac{1}{2}\right)x + 2 \][/tex]

Ordered Pairs:
[tex]\[ (3, 5) \][/tex]
[tex]\[ (4, 4) \][/tex]
[tex]\[ (5, 11) \][/tex]
[tex]\[ (6, 14) \][/tex]
[tex]\[ (2, 3) \][/tex]

Answer :

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GinnyAnswer GinnyAnswer · Answer 1 · 2024-08-06T11:56:19-04:00

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]