Question

find the slope of the line passing through the points (-7, 8) and (5, -7).

Explanation:

Step1: Recall slope formula

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \).
Let \((x_1, y_1)=(-7, 8)\) and \((x_2, y_2)=(5, -7)\).

Step2: Substitute values into formula

Substitute \( x_1=-7 \), \( y_1 = 8 \), \( x_2 = 5 \), \( y_2=-7 \) into the slope formula:
\( m=\frac{-7 - 8}{5 - (-7)} \)

Step3: Simplify numerator and denominator

Simplify numerator: \(-7 - 8=-15\)
Simplify denominator: \(5 - (-7)=5 + 7 = 12\)
So, \( m=\frac{-15}{12} \)

Step4: Reduce the fraction

Divide numerator and denominator by their greatest common divisor, which is 3:
\( m=\frac{-15\div3}{12\div3}=\frac{-5}{4} \)

Answer:

\(-\frac{5}{4}\)