Question

A line passes through the points in this table.
x y
9 3
10 12
11 21
12 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 that passes through the given points, we can use the formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\):

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

We can choose any two points from the table. Let's use the first two points:

1. \( (9, 3) \)
2. \( (10, 12) \)

Plugging these values into the slope formula:

\[
m = \frac{12 - 3}{10 - 9} = \frac{9}{1} = 9
\]

Now let's check the slope using the next pair of points, \( (10, 12) \) and \( (11, 21) \):

\[
m = \frac{21 - 12}{11 - 10} = \frac{9}{1} = 9
\]

Now using the points \( (11, 21) \) and \( (12, 30) \):

\[
m = \frac{30 - 21}{12 - 11} = \frac{9}{1} = 9
\]

Since the slope is consistent between the pairs of points, we conclude that the slope of the line is:

\[
\boxed{9}
\]