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 \( m=\frac{y_2 - y_1}{x_2 - x_1} \).
Here, \( (x_1, y_1)=(10, 6) \) and \( (x_2, y_2)=(6, 5) \).

Step2: Substitute the values into the formula

Substitute \( x_1 = 10 \), \( y_1 = 6 \), \( x_2 = 6 \), and \( y_2 = 5 \) into the slope formula:
\( m=\frac{5 - 6}{6 - 10} \)

Step3: Simplify the numerator and the denominator

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

Step4: Simplify the fraction

The negative signs in the numerator and the denominator cancel out, so \( \frac{-1}{-4}=\frac{1}{4} \)

Answer:

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