Question

A line passes through the points in this table.
x y
4 24
5 19
6 14
7 9
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 passing through the given points, we can use the formula for the slope \( m \) of a line, which is defined as:

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

We can pick any two points from the provided data. Let's use the points (4, 24) and (5, 19):

- For these points, \( (x_1, y_1) = (4, 24) \) and \( (x_2, y_2) = (5, 19) \).

Now we can substitute these values into the slope formula:

\[
m = \frac{19 - 24}{5 - 4} = \frac{-5}{1} = -5
\]

To confirm that the slope remains consistent across different pairs of points, we can check another pair, say (5, 19) and (6, 14):

- Here, \( (x_1, y_1) = (5, 19) \) and \( (x_2, y_2) = (6, 14) \).

Substituting these values in:

\[
m = \frac{14 - 19}{6 - 5} = \frac{-5}{1} = -5
\]

And checking another pair, for instance (6, 14) and (7, 9):

- For these points, \( (x_1, y_1) = (6, 14) \) and \( (x_2, y_2) = (7, 9) \).

Substituting these values in:

\[
m = \frac{9 - 14}{7 - 6} = \frac{-5}{1} = -5
\]

The slope is consistently \(-5\) when calculated across various pairs of points.

Therefore, the slope of the line that passes through the points in the table is:

\[
\boxed{-5}
\]