Question

A line passes through the points in this table.
\begin{tabular}{|c|c|}
\hline\( x \) & \( y \) \\
\hline 3 & 14 \\
\hline 4 & 20 \\
\hline 5 & 26 \\
\hline 6 & 32 \\
\hline
\end{tabular}
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 given in the table, we will use the slope formula:

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

We can choose any two points from the table. Let's use the points (3, 14) and (4, 20).

Here, \( (x_1, y_1) = (3, 14) \) and \( (x_2, y_2) = (4, 20) \).

Now, substitute these values into the slope formula:

\[
m = \frac{20 - 14}{4 - 3} = \frac{6}{1} = 6
\]

Thus, the slope of the line is

\[
\boxed{6}
\]

To ensure correctness, we can also check the slope using another pair of points, such as (4, 20) and (5, 26):

Using points (4, 20) and (5, 26):

\[
m = \frac{26 - 20}{5 - 4} = \frac{6}{1} = 6
\]

And again, using (5, 26) and (6, 32):

\[
m = \frac{32 - 26}{6 - 5} = \frac{6}{1} = 6
\]

Since the slope is consistent with all pairs chosen, we confirm that the slope of the line is

\[
\boxed{6}
\]