Question

a linear relationship is given in the table below.
-2 -3
3 -1
5\frac{1}{2} 0
8 1
13 3
determine the slope, m, of the relationship.
m = \square

Explanation:

Step1: Recall slope formula

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Choose two points

Let's take the points \((3, -1)\) and \((8, 1)\). Here, \( x_1 = 3 \), \( y_1=-1 \), \( x_2 = 8 \), \( y_2 = 1 \).

Step3: Calculate the slope

Substitute into the formula: \( m=\frac{1 - (-1)}{8 - 3}=\frac{1 + 1}{5}=\frac{2}{5} \). We can verify with another pair, say \((8, 1)\) and \((13, 3)\): \( m=\frac{3 - 1}{13 - 8}=\frac{2}{5} \), which is consistent.

Answer:

\(\frac{2}{5}\)