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 two points

We have points \((0, 2)\) and \((4, -5)\). Let \((x_1, y_1) = (0, 2)\) and \((x_2, y_2) = (4, -5)\).

Step3: Substitute into formula

Substitute into \( m = \frac{y_2 - y_1}{x_2 - x_1} \): \( m = \frac{-5 - 2}{4 - 0} \).

Step4: Simplify the expression

Calculate numerator: \(-5 - 2 = -7\). Denominator: \(4 - 0 = 4\). So \( m = \frac{-7}{4} \).

Answer:

\(-\frac{7}{4}\)