Question

or A line passes through the points in this table. x y 11 7 12 6 13 5 14 4 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:

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

Let's take two points from the table: (11, 7) and (12, 6).

Here, \( (x_1, y_1) = (11, 7) \) and \( (x_2, y_2) = (12, 6) \).

Now, we can substitute these values into the slope formula:

\[
m = \frac{6 - 7}{12 - 11} = \frac{-1}{1} = -1
\]

Thus, the slope of the line is

\[
\boxed{-1}
\]

We can also verify the slope by checking additional pairs of points.

Taking points (12, 6) and (13, 5):

\[
m = \frac{5 - 6}{13 - 12} = \frac{-1}{1} = -1
\]

Taking points (13, 5) and (14, 4):

\[
m = \frac{4 - 5}{14 - 13} = \frac{-1}{1} = -1
\]

The slope remains consistent. Therefore, the slope of the line that passes through these points is

\[
\boxed{-1}
\]