Question

x y
2 7
3 12
4 17
5 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 given the points \((2, 7)\), \((3, 12)\), \((4, 17)\), and \((5, 22)\), we can use the formula for the slope \(m\):

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

We can use any two points. Let’s take the points \((2, 7)\) and \((3, 12)\):

\[
m = \frac{12 - 7}{3 - 2} = \frac{5}{1} = 5
\]

Now, we can also check the slope between other pairs of points to confirm it is consistent:

1. Use points \((3, 12)\) and \((4, 17)\):

\[
m = \frac{17 - 12}{4 - 3} = \frac{5}{1} = 5
\]

2. Use points \((4, 17)\) and \((5, 22)\):

\[
m = \frac{22 - 17}{5 - 4} = \frac{5}{1} = 5
\]

Since the slope is consistent across all pairs, the slope of the line is

\[
\boxed{5}
\]