Question

what is the slope of the line that passes through the points (1, -9) and (4, -7)? 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 \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Identify coordinates

Let \( (x_1, y_1)=(1, - 9) \) and \( (x_2, y_2)=(4, - 7) \).

Step3: Substitute into formula

Substitute values: \( m=\frac{-7-(-9)}{4 - 1}=\frac{-7 + 9}{3}=\frac{2}{3} \).

Answer:

\(\frac{2}{3}\)