Question

what is the slope of the line that passes through the points (2, -4) and (5, 2)? write your answer in simplest form.

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 coordinates

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

Step3: Substitute into formula

Substitute the values into the slope formula: \( m=\frac{2-(-4)}{5 - 2}=\frac{2 + 4}{3}=\frac{6}{3} \).

Step4: Simplify

Simplify \(\frac{6}{3}\) to get \( 2 \).

Answer:

\( 2 \)