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 the two points

We have the points \((-4, -4)\) and \((4, 2)\). Let \((x_1, y_1) = (-4, -4)\) and \((x_2, y_2) = (4, 2)\).

Step3: Substitute into the formula

Substitute the values into the slope formula: \( m = \frac{2 - (-4)}{4 - (-4)} \).
Simplify the numerator and denominator: \( 2 - (-4) = 2 + 4 = 6 \), \( 4 - (-4) = 4 + 4 = 8 \). So \( m = \frac{6}{8} \).

Step4: Simplify the fraction

Simplify \(\frac{6}{8}\) by dividing numerator and denominator by their greatest common divisor, which is 2. So \( \frac{6 \div 2}{8 \div 2} = \frac{3}{4} \).

Answer:

\(\frac{3}{4}\)