Question

find the slope of the line that passes through (1, 3) and (6, 1). 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 coordinates

Here, \( x_1 = 1 \), \( y_1 = 3 \), \( x_2 = 6 \), \( y_2 = 1 \).

Step3: Substitute into formula

Substitute the values into the slope formula: \( m=\frac{1 - 3}{6 - 1} \).

Step4: Simplify numerator and denominator

Simplify the numerator: \( 1 - 3=-2 \). Simplify the denominator: \( 6 - 1 = 5 \). So, \( m=\frac{-2}{5} \) or \( -\frac{2}{5} \).

Answer:

\(-\frac{2}{5}\)