Question

what is the slope of the line that passes through the points (1, 6) and (13, 2)? write your answer in simplest form.

Explanation:

Step1: Recall slope formula

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

Step2: Identify coordinates

Here, \( x_1 = 1 \), \( y_1 = 6 \), \( x_2 = 13 \), \( y_2 = 2 \).

Step3: Substitute into formula

\( m=\frac{2 - 6}{13 - 1}=\frac{-4}{12} \).

Step4: Simplify the fraction

Divide numerator and denominator by 4: \( \frac{-4\div4}{12\div4}=\frac{-1}{3} \).

Answer:

\(-\frac{1}{3}\)