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

Step3: Substitute into the formula

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

Step4: Simplify the numerator and denominator

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

Answer:

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