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 points

We have points \((0, 4)\) (so \( x_1 = 0, y_1 = 4 \)) and \((3, -1)\) (so \( x_2 = 3, y_2 = -1 \)).

Step3: Substitute into formula

Substitute values into the slope formula: \( m=\frac{-1 - 4}{3 - 0} \).

Step4: Simplify numerator and denominator

Simplify numerator: \(-1 - 4=-5\). Simplify denominator: \(3 - 0 = 3\). So \( m=\frac{-5}{3}=-\frac{5}{3} \).

Answer:

\(-\frac{5}{3}\)