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

1 answer

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=83=5
    • Change in x=10=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.