Question

does this table represent a linear function if so state so and state the slope
x: 3,0,-3
y:1,2,3

Answer 1

To determine if the given table represents a linear function, we need to check if the change in \(y\) is proportional to the change in \(x\).

Here are the \(x\) and \(y\) values you've provided:

- When \(x = 3\), \(y = 1\)
- When \(x = 0\), \(y = 2\)
- When \(x = -3\), \(y = 3\)

Now, we will calculate the change in \(y\) for each change in \(x\):

1. From \(x = 3\) to \(x = 0\):
- Change in \(x = 0 - 3 = -3\)
- Change in \(y = 2 - 1 = 1\)
- Slope \(m = \frac{\text{change in } y}{\text{change in } x} = \frac{1}{-3} = -\frac{1}{3}\)

2. From \(x = 0\) to \(x = -3\):
- Change in \(x = -3 - 0 = -3\)
- Change in \(y = 3 - 2 = 1\)
- Slope \(m = \frac{\text{change in } y}{\text{change in } x} = \frac{1}{-3} = -\frac{1}{3}\)

Since the slope is consistent, the table does represent a linear function.

**Conclusion:** Yes, this table represents a linear function. The slope is \( -\frac{1}{3} \).