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

We have two points: \((x_1, y_1)=(-3, -2)\) and \((x_2, y_2)=(6, 4)\).

Step3: Substitute into the formula

Substitute the values into the slope formula: \( m=\frac{4 - (-2)}{6 - (-3)} \).
Simplify the numerator and denominator: \( 4 - (-2)=4 + 2 = 6 \) and \( 6 - (-3)=6 + 3 = 9 \). So, \( m=\frac{6}{9} \).

Step4: Simplify the fraction

Simplify \( \frac{6}{9} \) by dividing numerator and denominator by their greatest common divisor, which is 3. \( \frac{6\div3}{9\div3}=\frac{2}{3} \).

Answer:

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