A line passes through the points in this table.

\begin{tabular}{|c|c|}
\hline\( x \) & \( y \) \\
\hline 4 & 24 \\
\hline 5 & 19 \\
\hline 6 & 14 \\
\hline 7 & 9 \\
\hline
\end{tabular}
What is the slope of the line?
Write your answer as an integer or simplified fraction.

1 answer

To find the slope of the line passing 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 to calculate the slope. Let's choose the points \( (4, 24) \) and \( (5, 19) \).

Here, we have:

  • \( (x_1, y_1) = (4, 24) \)
  • \( (x_2, y_2) = (5, 19) \)

Now substituting these values into the slope formula:

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

To confirm the slope is consistent, let's also use the next pair of points \( (5, 19) \) and \( (6, 14) \):

Here, we have:

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

Calculating the slope:

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

Now, let's check the points \( (6, 14) \) and \( (7, 9) \):

Here, we have:

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

Calculating again:

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

In all cases, the slope is consistently \( -5 \).

Thus, the slope of the line is

\[ \boxed{-5} \]