Question

A line passes through the points in this table.
x y
8 8
20 6
32 4
44 2
What is the slope of the line?
Write your answer as an integer or simplified fraction.

Answer 1

To find the slope of the line that passes through the given points, we can use the formula for the slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \):

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

We can choose any two points from the table. Let's select the first two points: \( (8, 8) \) and \( (20, 6) \).

Here, \( x_1 = 8 \), \( y_1 = 8 \), \( x_2 = 20 \), and \( y_2 = 6 \).

Now we can calculate the slope:

\[
m = \frac{6 - 8}{20 - 8} = \frac{-2}{12} = \frac{-1}{6}
\]

Thus, the slope of the line is:

\[
\boxed{-\frac{1}{6}}
\]

To ensure the slope is consistent, we can calculate it with another pair of points. Let's check \( (20, 6) \) and \( (32, 4) \):

\[
m = \frac{4 - 6}{32 - 20} = \frac{-2}{12} = \frac{-1}{6}
\]

Now let's check with \( (32, 4) \) and \( (44, 2) \):

\[
m = \frac{2 - 4}{44 - 32} = \frac{-2}{12} = \frac{-1}{6}
\]

And finally, using the first and last points, \( (8, 8) \) and \( (44, 2) \):

\[
m = \frac{2 - 8}{44 - 8} = \frac{-6}{36} = \frac{-1}{6}
\]

All slopes calculated yield the same result. Therefore, the slope of the line is:

\[
\boxed{-\frac{1}{6}}
\]