Question

what is the slope of the line that passes through the points (9,5) and (21, -5)? write your answer in simplest form.

Explanation:

Step1: Recall slope formula

The slope \( m \) of a line passing through 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: Identify coordinates

Here, \( x_1 = 9 \), \( y_1 = 5 \), \( x_2 = 21 \), \( y_2=-5 \).

Step3: Substitute into formula

\( m=\frac{-5 - 5}{21 - 9}=\frac{-10}{12} \).

Step4: Simplify fraction

Divide numerator and denominator by 2: \( m =-\frac{5}{6} \).

Answer:

\(-\frac{5}{6}\)