Question

A line passes through the points in this table.
x y
14 14
15 16
16 18
17 20
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 given the points in the table, we can use the formula for slope \( m \) given two points \((x_1, y_1)\) and \((x_2, y_2)\):

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

We can use any two points from the provided points. Let's use the first two points: \((14, 14)\) and \((15, 16)\).

Setting \((x_1, y_1) = (14, 14)\) and \((x_2, y_2) = (15, 16)\):

\[
m = \frac{16 - 14}{15 - 14} = \frac{2}{1} = 2
\]

Now, let's check with the next pair of points: \((15, 16)\) and \((16, 18)\).

Setting \((x_1, y_1) = (15, 16)\) and \((x_2, y_2) = (16, 18)\):

\[
m = \frac{18 - 16}{16 - 15} = \frac{2}{1} = 2
\]

We can verify again with the pair \((16, 18)\) and \((17, 20)\):

Setting \((x_1, y_1) = (16, 18)\) and \((x_2, y_2) = (17, 20)\):

\[
m = \frac{20 - 18}{17 - 16} = \frac{2}{1} = 2
\]

The slope is consistent across these pairs. Therefore, the slope of the line is

\[
\boxed{2}
\]