Question

A linear relationship is given in the table below.
-2,-3
3,-1
5 1/2, 0
8,1
13, 3






























Determine the slope,
m, of the relationship.

Answer 1

To determine the slope \( m \) of a linear relationship given by two points, we can use the formula:

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

Let’s choose the points \((-2, -3)\) and \((8, 1)\) from the table.

Here, we have:
- \( (x_1, y_1) = (-2, -3) \)
- \( (x_2, y_2) = (8, 1) \)

Substituting these values into the slope formula:

\[
m = \frac{1 - (-3)}{8 - (-2)} = \frac{1 + 3}{8 + 2} = \frac{4}{10} = \frac{2}{5}
\]

Thus, the slope \( m \) of the relationship is:

\[
\boxed{\frac{2}{5}}
\]