Question

find the slope of the line that passes through (9, 10) and (2, 1). 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, \( (x_1, y_1)=(9, 10) \) and \( (x_2, y_2)=(2, 1) \).

Step2: Substitute the values into the formula

Substitute \( x_1 = 9 \), \( y_1 = 10 \), \( x_2 = 2 \), and \( y_2 = 1 \) into the slope formula:
\( m=\frac{1 - 10}{2 - 9} \)

Step3: Simplify the numerator and the denominator

First, simplify the numerator: \( 1-10=-9 \)
Then, simplify the denominator: \( 2 - 9=-7 \)
So, \( m=\frac{-9}{-7} \)

Step4: Simplify the fraction

The negative signs in the numerator and the denominator cancel out, so \( m = \frac{9}{7} \)

Answer:

\( \frac{9}{7} \)