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 points

We have two points: \((-4, 1)\) (so \( x_1 = -4, y_1 = 1 \)) and \((4, -1)\) (so \( x_2 = 4, y_2 = -1 \)).

Step3: Substitute into formula

Substitute the values into the slope formula: \( m = \frac{-1 - 1}{4 - (-4)} \).

Step4: Simplify numerator and denominator

Simplify numerator: \( -1 - 1 = -2 \). Simplify denominator: \( 4 - (-4) = 4 + 4 = 8 \). So \( m = \frac{-2}{8} \).

Step5: Reduce the fraction

Simplify \( \frac{-2}{8} \) by dividing numerator and denominator by their greatest common divisor, which is 2. So \( \frac{-2 \div 2}{8 \div 2} = \frac{-1}{4} \).

Answer:

\(-\frac{1}{4}\)