Question

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

Answer 1

To determine if the points represent a linear function, we can check if the change in \( y \) (the vertical change) over the change in \( x \) (the horizontal change) is constant.

You have two points:
1. \((-4, 1)\)
2. \((0, 2)\)

Now, let's calculate the slope \( m \) using the formula for slope:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Plugging in the coordinates of the points:

- \( (x_1, y_1) = (-4, 1) \)
- \( (x_2, y_2) = (0, 2) \)

\[
m = \frac{2 - 1}{0 - (-4)} = \frac{1}{4}
\]

Since you have a constant slope, the table does represent a linear function.

Therefore, **yes**, it is a linear function, and the **slope** is \( \frac{1}{4} \).