Question

find the slope of the line that passes through (6, 1) and (3, 5). simplify your answer and write it as a proper fraction, improper fraction, or integer.

Explanation:

Step1: Recall the slope formula

The slope \( m \) of a line passing through two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).
Here, \( (x_1, y_1)=(6, 1) \) and \( (x_2, y_2)=(3, 5) \).

Step2: Substitute the values into the formula

Substitute \( x_1 = 6 \), \( y_1 = 1 \), \( x_2 = 3 \), and \( y_2 = 5 \) into the slope formula:
\( m=\frac{5 - 1}{3 - 6} \)

Step3: Simplify the numerator and the denominator

First, simplify the numerator: \( 5 - 1=4 \).
Then, simplify the denominator: \( 3 - 6=-3 \).
So, \( m = \frac{4}{-3}=-\frac{4}{3} \)

Answer:

\(-\frac{4}{3}\)