Question

A line passes through the points in this table.
x y
2 9
9 16
16 23
23 30
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 can use the slope formula:

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

We can use any two points from the table. Let's use the first and the last points: (2, 9) and (23, 30).

Here, \( (x_1, y_1) = (2, 9) \) and \( (x_2, y_2) = (23, 30) \).

Substituting these values into the slope formula gives:

\[
m = \frac{30 - 9}{23 - 2} = \frac{21}{21} = 1
\]

Thus, the slope of the line is

\[
\boxed{1}.
\]

We can double-check using another pair of points. Let's use the second and the third points: (9, 16) and (16, 23).

Here, \( (x_1, y_1) = (9, 16) \) and \( (x_2, y_2) = (16, 23) \).

Calculating the slope gives:

\[
m = \frac{23 - 16}{16 - 9} = \frac{7}{7} = 1
\]

All pairs yield the same slope, confirming that the slope of the line is indeed

\[
\boxed{1}.
\]