Question

find the slope of the line that passes through (8, 28) and (92, -6). simplify your answer and write it as a proper fraction, improper fraction, or integer.

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

Let \( (x_1, y_1)=(8, 28) \) and \( (x_2, y_2)=(92, -6) \).

Step3: Substitute into formula

Substitute values: \( m=\frac{-6 - 28}{92 - 8} \).

Step4: Simplify numerator and denominator

Numerator: \( -6 - 28=-34 \). Denominator: \( 92 - 8 = 84 \). So \( m=\frac{-34}{84} \).

Step5: Reduce the fraction

Divide numerator and denominator by 2: \( m =-\frac{17}{42} \).

Answer:

\(-\frac{17}{42}\)