Question

A line passes through the points in this table.
x y
8 24
9 17
10 10
11 3
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 any two points from the table. The slope \( m \) is calculated using the formula:

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

Let's use the first two points (8, 24) and (9, 17):

- \( (x_1, y_1) = (8, 24) \)
- \( (x_2, y_2) = (9, 17) \)

Now we can substitute these values into the slope formula:

\[
m = \frac{17 - 24}{9 - 8} = \frac{-7}{1} = -7
\]

Now let's verify the slope using another pair of points, say (10, 10) and (11, 3):

- \( (x_1, y_1) = (10, 10) \)
- \( (x_2, y_2) = (11, 3) \)

Using the slope formula again:

\[
m = \frac{3 - 10}{11 - 10} = \frac{-7}{1} = -7
\]

Both calculations yield the same slope. Thus, the slope of the line is:

\[
\boxed{-7}
\]