Linear Function Verification: Is the Table of X = [-1, 2, 6] and Y = [1, 2, 3] Consistent?

To determine if the table represents a linear function, we need to check if the slope between each consecutive pair of points is constant.
Using the slope formula $m = \frac{y_2 - y_1}{x_2 - x_1}$, we calculate:

• Between points $(-1, 1)$ and $(2, 2)$:
  $m = \frac{2 - 1}{2 - (-1)} = \frac{1}{3}$
• Between points $(2, 2)$ and $(6, 3)$:
  $m = \frac{3 - 2}{6 - 2} = \frac{1}{4}$

Since the slopes are not equal ($\frac{1}{3} \neq \frac{1}{4}$), the function is not linear.

Thus, the table does not represent a linear function.