Question

find the slope of the line that passes through (10, 10) and (6, 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, \( (x_1,y_1)=(10,10) \) and \( (x_2,y_2)=(6,1) \).

Step2: Substitute the values into the formula

Substitute \( x_1 = 10 \), \( y_1 = 10 \), \( x_2 = 6 \), and \( y_2 = 1 \) into the slope formula: \( m=\frac{1 - 10}{6 - 10} \).

Step3: Simplify the numerator and the denominator

Calculate the numerator: \( 1-10=-9 \). Calculate the denominator: \( 6 - 10=-4 \). So, \( m=\frac{-9}{-4} \).

Step4: Simplify the fraction

A negative divided by a negative is positive, so \( \frac{-9}{-4}=\frac{9}{4} \).

Answer:

\( \frac{9}{4} \)