Question

find the slope of the line that passes through (10, 9) and (4, 4). simplify your answer and write it as a proper fraction, improper fraction, or integer.

Explanation:

Step1: Recall 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 coordinates

Let \( (x_1, y_1)=(10, 9) \) and \( (x_2, y_2)=(4, 4) \).

Step3: Substitute into formula

Substitute the values into the slope formula: \( m=\frac{4 - 9}{4 - 10} \).

Step4: Simplify numerator and denominator

Simplify the numerator: \( 4 - 9=-5 \).
Simplify the denominator: \( 4 - 10=-6 \).
So, \( m = \frac{-5}{-6}=\frac{5}{6} \).

Answer:

\(\frac{5}{6}\)