Question

A line passes through the points in this table.
x y
10 6
13 21
16 36
19 51
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 \((10, 6)\) and \((13, 21)\):

- \( x_1 = 10 \), \( y_1 = 6 \)
- \( x_2 = 13 \), \( y_2 = 21 \)

Now, we can plug these values into the slope formula:

\[
m = \frac{21 - 6}{13 - 10} = \frac{15}{3} = 5
\]

Let's confirm the slope using another pair of points. We'll use \((16, 36)\) and \((19, 51)\):

- \( x_1 = 16 \), \( y_1 = 36 \)
- \( x_2 = 19 \), \( y_2 = 51 \)

Calculating the slope:

\[
m = \frac{51 - 36}{19 - 16} = \frac{15}{3} = 5
\]

Since both pairs of points give us the same slope, we can conclude that the slope of the line is:

\[
\boxed{5}
\]