Question

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

Answer 1

To determine if the data represents a linear function, we need to check if the change in \( y \) over the change in \( x \) (i.e., the slope) is consistent.

The given points are:
- Point 1: \( (-1, -2) \)
- Point 2: \( (1, 1) \)

Now, we can calculate the slope \( m \) using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Plugging in the coordinates of the points:
\[
m = \frac{1 - (-2)}{1 - (-1)} = \frac{1 + 2}{1 + 1} = \frac{3}{2}
\]

Since the slope \( \frac{3}{2} \) is constant for the two points, this indicates that the points represent a linear function.

**Conclusion:** Yes, this table represents a linear function, and the slope is \( \frac{3}{2} \).