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 \((-3, -3)\) and \((3, -5)\). Let \((x_1, y_1)=(-3, -3)\) and \((x_2, y_2)=(3, -5)\).

Step3: Substitute into formula

Substitute into the slope formula: \( m = \frac{-5 - (-3)}{3 - (-3)} \).
Simplify numerator and denominator: \( m = \frac{-5 + 3}{3 + 3} = \frac{-2}{6} \).

Step4: Simplify the fraction

Simplify \(\frac{-2}{6}\) to \(-\frac{1}{3}\).

Answer:

\(-\frac{1}{3}\)