Question

The ordered pairs in the table below represent a linear function.

x
y
6
2
9
8

What is the slope of the function?
One-fourth
One-half
2
4

Answer 1

To find the slope of a linear function represented by two points (x₁, y₁) and (x₂, y₂), we can use the formula for the slope \( m \):

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

From the table, we have the ordered pairs as follows:

1. (6, 2)
2. (9, 8)

Now, we can assign these points:

- \( x_1 = 6, y_1 = 2 \)
- \( x_2 = 9, y_2 = 8 \)

Now substitute these values into the slope formula:

\[
m = \frac{8 - 2}{9 - 6} = \frac{6}{3} = 2
\]

Therefore, the slope of the function is \( 2 \).