QQuestionMathematics
QuestionMathematics
Which table represents a linear function?
| *x* | *y* | *x* | *y* | *x* | *y* | *x* | *y* |
| --- | --- | --- | --- | --- | --- | --- | --- |
| 1 | −2 | 1 | −2 | 1 | −2 | 1 | −2 |
| 2 | −6 | 2 | −5 | 2 | −10 | 2 | −4 |
| 3 | −2 | 3 | −9 | 3 | −18 | 3 | −8 |
| 4 | −6 | 4 | −14 | 4 | −26 | 4 | −16 |
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Answer
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Step 1:I'll solve this systematically by checking each table for linearity.
Step 2:: Recall the definition of a linear function
- The change in $$y$$ is proportional to the change in $$x
- m is the slope (constant rate of change)
Step 3:: Check first table's linearity
- Next points confirm consistent slope of $$-4
- x = 2, y = - 6 - This table represents a linear function
Step 4:: Check second table's linearity
- Slope between first two points: $$\frac{-5 - (-2)}{2 - 1} = -3
- Inconsistent slope between points - NOT a linear function
Step 5:: Check third table's linearity
- Slope between first two points: $$\frac{-10 - (-2)}{2 - 1} = -8
- Inconsistent slope between points - NOT a linear function
Step 6:: Check fourth table's linearity
- Slope between first two points: $$\frac{-4 - (-2)}{2 - 1} = -2
- Inconsistent slope between points - NOT a linear function
Final Answer
The first table represents a linear function, with slope - 4 and equation y = - 4x + (- 2).
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