Question

A line passes through the points in this table.
x y
5 16
10 13
20 7
30 1
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 choose any two points from the table. Let's use the first point (5, 16) and the last point (30, 1).

Using these points:
- \( (x_1, y_1) = (5, 16) \)
- \( (x_2, y_2) = (30, 1) \)

Now substituting these values into the slope formula:

\[
m = \frac{1 - 16}{30 - 5} = \frac{-15}{25} = \frac{-3}{5}
\]

Thus, the slope of the line is

\[
\boxed{-\frac{3}{5}}
\]