Question

does this table represent a linear function if so state so and state the slope
x:-2,-1,0,1
y:-4,-1,3,8

Answer 1

To determine if the given table of values represents a linear function, we need to check if the differences between the \(y\) values are consistent for equal intervals of the \(x\) values.

The given values are:
- When \(x = -2\), \(y = -4\)
- When \(x = -1\), \(y = -1\)
- When \(x = 0\), \(y = 3\)
- When \(x = 1\), \(y = 8\)

We can calculate the differences in \(y\) and the corresponding differences in \(x\):

1. From \(x = -2\) to \(x = -1\):
- Change in \(y = -1 - (-4) = 3\)
- Change in \(x = -1 - (-2) = 1\)

2. From \(x = -1\) to \(x = 0\):
- Change in \(y = 3 - (-1) = 4\)
- Change in \(x = 0 - (-1) = 1\)

3. From \(x = 0\) to \(x = 1\):
- Change in \(y = 8 - 3 = 5\)
- Change in \(x = 1 - 0 = 1\)

Now let's summarize the changes:
- From \(-4\) to \(-1\): Increase of \(3\)
- From \(-1\) to \(3\): Increase of \(4\)
- From \(3\) to \(8\): Increase of \(5\)

The changes in \(y\) are \(3\), \(4\), and \(5\) respectively, which are not constant. Since the differences in \(y\) are not consistent, this indicates that the function is **not linear**.

In conclusion, the table does not represent a linear function.