Question

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 calculate the slope of the line using the given points, we can use the formula for the slope (m) between two points \((x_1, y_1)\) and \((x_2, y_2)\):

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

Let's take the first two points \((9, 7)\) and \((19, 12)\):

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

Now, substitute these values into the slope formula:

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

To confirm that this slope applies to the other points, we can calculate it using another pair of points, say \((19, 12)\) and \((29, 17)\):

- \(x_1 = 19\), \(y_1 = 12\)
- \(x_2 = 29\), \(y_2 = 17\)

Now, substitute these values into the slope formula:

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

The same calculation applies for the other points, therefore the slope of the line is:

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