Question

A line passes through the points in this table.
x y
3 14
4 20
5 26
6 32
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 given in the table, 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 use any two points from the table. Let's choose the points \((3, 14)\) and \((4, 20)\).

Here, \((x_1, y_1) = (3, 14)\) and \((x_2, y_2) = (4, 20)\).

Substituting the values into the slope formula:

\[
m = \frac{20 - 14}{4 - 3} = \frac{6}{1} = 6
\]

Thus, the slope of the line is \( \boxed{6} \).

We can verify this slope using another pair of points, such as \((4, 20)\) and \((5, 26)\):

\[
m = \frac{26 - 20}{5 - 4} = \frac{6}{1} = 6
\]

And also using \((5, 26)\) and \((6, 32)\):

\[
m = \frac{32 - 26}{6 - 5} = \frac{6}{1} = 6
\]

In all cases, the slope consistently equals 6, confirming that the slope of the line is \( \boxed{6} \).