Question

does this table represent a linear function if so state so and state the slope
x:-14,-10,-5,-4
y:-11,-7,-2,-1

Answer 1

To determine if the given table represents a linear function, we can check if the change in \( y \) values is proportional to the change in \( x \) values. This can be done by calculating the slopes between consecutive points.

Given the points:
- \((-14, -11)\)
- \((-10, -7)\)
- \((-5, -2)\)
- \((-4, -1)\)

Let's calculate the slope \( m \) between each pair of successive points using the formula:

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

1. Between \((-14, -11)\) and \((-10, -7)\):
\[
m_1 = \frac{-7 - (-11)}{-10 - (-14)} = \frac{-7 + 11}{-10 + 14} = \frac{4}{4} = 1
\]

2. Between \((-10, -7)\) and \((-5, -2)\):
\[
m_2 = \frac{-2 - (-7)}{-5 - (-10)} = \frac{-2 + 7}{-5 + 10} = \frac{5}{5} = 1
\]

3. Between \((-5, -2)\) and \((-4, -1)\):
\[
m_3 = \frac{-1 - (-2)}{-4 - (-5)} = \frac{-1 + 2}{-4 + 5} = \frac{1}{1} = 1
\]

Since the slope \( m \) is the same (1) between all pairs of points, we can conclude that the table does represent a linear function.

**Conclusion:**
Yes, this table represents a linear function, and the slope is \( 1 \).