Question

find the slope of the line that passes through (10, 6) and (6, 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 \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Identify the coordinates

Let \( (x_1, y_1)=(10, 6) \) and \( (x_2, y_2)=(6, 5) \).

Step3: Substitute into the formula

Substitute the values into the slope formula: \( m=\frac{5 - 6}{6 - 10} \).

Step4: Simplify the numerator and denominator

Simplify the numerator: \( 5 - 6=- 1 \).
Simplify the denominator: \( 6 - 10=-4 \).
So, \( m = \frac{-1}{-4}=\frac{1}{4} \).

Answer:

\(\frac{1}{4}\)