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 \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Identify two points

From the graph, we have points \((-8, -12)\) and \((8, -4)\). Let \((x_1, y_1)=(-8, -12)\) and \((x_2, y_2)=(8, -4)\).

Step3: Substitute into formula

Substitute values into the slope formula: \( m=\frac{-4 - (-12)}{8 - (-8)} \).
Simplify 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 8: \( \frac{8\div8}{16\div8}=\frac{1}{2} \).

Answer:

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