Question

A line passes through the points in this table.
x y
4 17
5 4
6 -9
7 -22
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 will use the formula for the slope \( m \):

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

We can choose any two points from the table. Let's select the first two points: \( (4, 17) \) and \( (5, 4) \):

- \( x_1 = 4 \), \( y_1 = 17 \)
- \( x_2 = 5 \), \( y_2 = 4 \)

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

\[
m = \frac{4 - 17}{5 - 4} = \frac{-13}{1} = -13
\]

We can verify this slope by calculating it using another pair of points. Let's use the points \( (5, 4) \) and \( (6, -9) \):

- \( x_1 = 5 \), \( y_1 = 4 \)
- \( x_2 = 6 \), \( y_2 = -9 \)

Plugging in these values:

\[
m = \frac{-9 - 4}{6 - 5} = \frac{-13}{1} = -13
\]

Finally, we can check one more pair, \( (6, -9) \) and \( (7, -22) \):

- \( x_1 = 6 \), \( y_1 = -9 \)
- \( x_2 = 7 \), \( y_2 = -22 \)

Calculating the slope:

\[
m = \frac{-22 - (-9)}{7 - 6} = \frac{-22 + 9}{1} = \frac{-13}{1} = -13
\]

Since the slope is consistent across all pairs of points, we conclude that the slope of the line is

\[
\boxed{-13}
\]