Question

A line passes through the points in this table.
x y
9 7
19 12
29 17
39 22
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 slope (\(m\)) between two points \((x_1, y_1)\) and \((x_2, y_2)\):

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

Let's calculate the slope using the first two points from the table: \((9, 7)\) and \((19, 12)\).

Here,

- \(x_1 = 9, y_1 = 7\)
- \(x_2 = 19, y_2 = 12\)

Now substitute these values into the slope formula:

\[
m = \frac{12 - 7}{19 - 9} = \frac{5}{10} = \frac{1}{2}
\]

To verify, we can calculate the slope using the other consecutive points, for example, \((19, 12)\) and \((29, 17)\):

\[
m = \frac{17 - 12}{29 - 19} = \frac{5}{10} = \frac{1}{2}
\]

And again with points \((29, 17)\) and \((39, 22)\):

\[
m = \frac{22 - 17}{39 - 29} = \frac{5}{10} = \frac{1}{2}
\]

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

\[
\boxed{\frac{1}{2}}
\]