Question

A line passes through the points in this table.
x y
0 2
9 6
27 14
54 26
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 points in the table, we can use the formula for the slope \(m\) between any two points \((x_1, y_1)\) and \((x_2, y_2)\):

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

We can select any two points from the table. Let's use the first point \((0, 2)\) and the second point \((9, 6)\):

Here,
- \(x_1 = 0\), \(y_1 = 2\)
- \(x_2 = 9\), \(y_2 = 6\)

Now substituting these values into the slope formula:

\[
m = \frac{6 - 2}{9 - 0} = \frac{4}{9}
\]

Now we can double-check this with another pair of points. Let's use the points \((9, 6)\) and \((27, 14)\):

Here,
- \(x_1 = 9\), \(y_1 = 6\)
- \(x_2 = 27\), \(y_2 = 14\)

Now substituting these values into the slope formula:

\[
m = \frac{14 - 6}{27 - 9} = \frac{8}{18} = \frac{4}{9}
\]

And one more check with the points \((27, 14)\) and \((54, 26)\):

Here,
- \(x_1 = 27\), \(y_1 = 14\)
- \(x_2 = 54\), \(y_2 = 26\)

Substituting into the slope formula:

\[
m = \frac{26 - 14}{54 - 27} = \frac{12}{27} = \frac{4}{9}
\]

In every case, we find the slope \(m\) to be \(\frac{4}{9}\).

Thus, the slope of the line is

\[
\boxed{\frac{4}{9}}
\]