does this table represent a linear function if so state so and state the slope

Question

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.