Question

A line passes through the points in this table.
x y
7 31
8 23
9 15
10 7
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 points given in the table, we can use the formula for the slope \( m \), which is defined as:

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

We can select any two points from the table. Let's use the first two points \( (7, 31) \) and \( (8, 23) \).

Here:
- \( x_1 = 7 \), \( y_1 = 31 \)
- \( x_2 = 8 \), \( y_2 = 23 \)

Now we can substitute these values into the slope formula:

\[
m = \frac{23 - 31}{8 - 7} = \frac{-8}{1} = -8
\]

To verify, we can calculate the slope using the other pairs of points:

Using \( (8, 23) \) and \( (9, 15) \):

\[
m = \frac{15 - 23}{9 - 8} = \frac{-8}{1} = -8
\]

Using \( (9, 15) \) and \( (10, 7) \):

\[
m = \frac{7 - 15}{10 - 9} = \frac{-8}{1} = -8
\]

In all cases, the slope remains consistent, confirming our calculations.

Thus, the slope of the line is:

\[
\boxed{-8}
\]