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 points in the table, you can use the formula for the slope \( m \) given two points \((x_1, y_1)\) and \((x_2, y_2)\):

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

Let's use the first two points from the table: (4, 24) and (5, 19).

Here, \((x_1, y_1) = (4, 24)\) and \((x_2, y_2) = (5, 19)\).

Now substitute the values into the slope formula:

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

The slope of the line is \(-5\).

We can confirm this with another pair of points, say (5, 19) and (6, 14):

Using these points:

\((x_1, y_1) = (5, 19)\) and \((x_2, y_2) = (6, 14)\):

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

Finally, checking the next pair (6, 14) and (7, 9):

Using these points:

\((x_1, y_1) = (6, 14)\) and \((x_2, y_2) = (7, 9)\):

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

All pairs yield the same slope.

Thus, the slope of the line is \(\boxed{-5}\).