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 two points: \((-9, 0)\) and \((9, -12)\). Let \((x_1, y_1)=(-9, 0)\) and \((x_2, y_2)=(9, -12)\).

Step3: Substitute into formula

Substitute \( x_1=-9 \), \( y_1 = 0 \), \( x_2=9 \), \( y_2=-12 \) into the slope formula:
\( m=\frac{-12 - 0}{9 - (-9)}=\frac{-12}{18} \).

Step4: Simplify the fraction

Simplify \( \frac{-12}{18} \) by dividing numerator and denominator by their greatest common divisor, which is 6. So \( \frac{-12\div6}{18\div6}=\frac{-2}{3} \).

Answer:

\(-\frac{2}{3}\)