Question
Choose ,begin emphasis,all,end emphasis, the tables that represent a linear function.
Answer options with 5 options
A.
x
negative 3
negative 1
2
5
y
negative 5
negative 1
5
11
B.
x
negative 4
negative 2
1
4
y
negative 6
negative 2
2
6
C.
x
negative 3
negative 1
1
4
y
9
1
1
16
D.
x
negative 4
negative 1
1
3
y
3
3
3
3
E.
x
negative 5
negative 2
2
4
y
10
4
negative 4
negative 8
Answer options with 5 options
A.
x
negative 3
negative 1
2
5
y
negative 5
negative 1
5
11
B.
x
negative 4
negative 2
1
4
y
negative 6
negative 2
2
6
C.
x
negative 3
negative 1
1
4
y
9
1
1
16
D.
x
negative 4
negative 1
1
3
y
3
3
3
3
E.
x
negative 5
negative 2
2
4
y
10
4
negative 4
negative 8
Answers
GPT-4o mini
To determine which tables represent a linear function, we need to check if there is a consistent rate of change in the y-values for every unit increase in the x-values.
**A:**
x: -3, -1, 2, 5
y: -5, -1, 5, 11
- Change in x from -3 to -1: +2 (Change in y: -5 to -1 = +4) → slope = 4/2 = 2
- Change in x from -1 to 2: +3 (Change in y: -1 to 5 = +6) → slope = 6/3 = 2
- Change in x from 2 to 5: +3 (Change in y: 5 to 11 = +6) → slope = 6/3 = 2
The slopes are not consistent; this is *not* a linear function.
---
**B:**
x: -4, -2, 1, 4
y: -6, -2, 2, 6
- Change in x from -4 to -2: +2 (Change in y: -6 to -2 = +4) → slope = 4/2 = 2
- Change in x from -2 to 1: +3 (Change in y: -2 to 2 = +4) → slope = 4/3 (not equal to previous slope)
- Change in x from 1 to 4: +3 (Change in y: 2 to 6 = +4) → slope = 4/3 (not equal to previous slope)
The slopes are not consistent; this is *not* a linear function.
---
**C:**
x: -3, -1, 1, 4
y: 9, 1, 1, 16
- Change in x from -3 to -1: +2 (Change in y: 9 to 1 = -8) → slope = -8/2 = -4
- Change in x from -1 to 1: +2 (Change in y: 1 to 1 = 0) → slope = 0/2 = 0
- Change in x from 1 to 4: +3 (Change in y: 1 to 16 = +15) → slope = 15/3 = 5
The slopes are not consistent; this is *not* a linear function.
---
**D:**
x: -4, -1, 1, 3
y: 3, 3, 3, 3
- All y-values are the same (3) regardless of x-value, which means the slope is 0.
This is a constant function and thus a linear function.
---
**E:**
x: -5, -2, 2, 4
y: 10, 4, -4, -8
- Change in x from -5 to -2: +3 (Change in y: 10 to 4 = -6) → slope = -6/3 = -2
- Change in x from -2 to 2: +4 (Change in y: 4 to -4 = -8) → slope = -8/4 = -2
- Change in x from 2 to 4: +2 (Change in y: -4 to -8 = -4) → slope = -4/2 = -2
The slopes are consistent; this is a linear function.
---
**Final Answer: The tables that represent a linear function are:**
**D and E.**
**A:**
x: -3, -1, 2, 5
y: -5, -1, 5, 11
- Change in x from -3 to -1: +2 (Change in y: -5 to -1 = +4) → slope = 4/2 = 2
- Change in x from -1 to 2: +3 (Change in y: -1 to 5 = +6) → slope = 6/3 = 2
- Change in x from 2 to 5: +3 (Change in y: 5 to 11 = +6) → slope = 6/3 = 2
The slopes are not consistent; this is *not* a linear function.
---
**B:**
x: -4, -2, 1, 4
y: -6, -2, 2, 6
- Change in x from -4 to -2: +2 (Change in y: -6 to -2 = +4) → slope = 4/2 = 2
- Change in x from -2 to 1: +3 (Change in y: -2 to 2 = +4) → slope = 4/3 (not equal to previous slope)
- Change in x from 1 to 4: +3 (Change in y: 2 to 6 = +4) → slope = 4/3 (not equal to previous slope)
The slopes are not consistent; this is *not* a linear function.
---
**C:**
x: -3, -1, 1, 4
y: 9, 1, 1, 16
- Change in x from -3 to -1: +2 (Change in y: 9 to 1 = -8) → slope = -8/2 = -4
- Change in x from -1 to 1: +2 (Change in y: 1 to 1 = 0) → slope = 0/2 = 0
- Change in x from 1 to 4: +3 (Change in y: 1 to 16 = +15) → slope = 15/3 = 5
The slopes are not consistent; this is *not* a linear function.
---
**D:**
x: -4, -1, 1, 3
y: 3, 3, 3, 3
- All y-values are the same (3) regardless of x-value, which means the slope is 0.
This is a constant function and thus a linear function.
---
**E:**
x: -5, -2, 2, 4
y: 10, 4, -4, -8
- Change in x from -5 to -2: +3 (Change in y: 10 to 4 = -6) → slope = -6/3 = -2
- Change in x from -2 to 2: +4 (Change in y: 4 to -4 = -8) → slope = -8/4 = -2
- Change in x from 2 to 4: +2 (Change in y: -4 to -8 = -4) → slope = -4/2 = -2
The slopes are consistent; this is a linear function.
---
**Final Answer: The tables that represent a linear function are:**
**D and E.**