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 the 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 two points

From the graph, we have the points \((-3, -1)\) and \((3, 1)\). Let \((x_1, y_1)=(-3, -1)\) and \((x_2, y_2)=(3, 1)\).

Step3: Substitute into the slope formula

Substitute the values into the formula: \( m=\frac{1 - (-1)}{3 - (-3)} \).
Simplify the numerator and denominator: \( 1-(-1)=1 + 1 = 2 \) and \( 3-(-3)=3 + 3 = 6 \). So \( m=\frac{2}{6} \).

Step4: Simplify the fraction

Simplify \( \frac{2}{6} \) by dividing both the numerator and denominator by their greatest common divisor, which is 2. So \( \frac{2\div2}{6\div2}=\frac{1}{3} \).

Answer:

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