Question

what is the slope of this line? 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 given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Identify the points

Let \((x_1, y_1)=(-8, -12)\) and \((x_2, y_2)=(8, -4)\).

Step3: Substitute into formula

Substitute the values into the slope formula: \( m=\frac{-4 - (-12)}{8 - (-8)} \).
Simplify the numerator and denominator: \( -4 - (-12)=-4 + 12 = 8 \), \( 8 - (-8)=8 + 8 = 16 \).
So, \( m=\frac{8}{16} \).

Step4: Simplify the fraction

Simplify \(\frac{8}{16}\) by dividing numerator and denominator by their greatest common divisor, which is 8. \(\frac{8\div8}{16\div8}=\frac{1}{2}\).

Answer:

\(\frac{1}{2}\)