Question

find the slope of the line that passes through (100, 100) and (22, 6). simplify your answer and write it as a proper fraction, improper fraction, or integer.

Explanation:

Step1: Recall slope formula

The slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is \( m = \frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Identify coordinates

Let \( (x_1, y_1) = (100, 100) \) and \( (x_2, y_2) = (22, 6) \).

Step3: Substitute into formula

\( m = \frac{6 - 100}{22 - 100} = \frac{-94}{-78} \).

Step4: Simplify fraction

Simplify \( \frac{-94}{-78} \) by dividing numerator and denominator by their greatest common divisor, which is 2. So \( \frac{94\div2}{78\div2} = \frac{47}{39} \).

Answer:

\(\frac{47}{39}\)