Question

find the slope of the line that passes through (52, 68) and (-24, 28). 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 \( m=\frac{y_2 - y_1}{x_2 - x_1} \).
Let \( (x_1, y_1)=(52, 68) \) and \( (x_2, y_2)=(-24, 28) \).

Step2: Substitute values into formula

Substitute \( x_1 = 52 \), \( y_1 = 68 \), \( x_2=-24 \), \( y_2 = 28 \) into the slope formula:
\( m=\frac{28 - 68}{-24 - 52} \)

Step3: Simplify numerator and denominator

Calculate numerator: \( 28-68=-40 \)
Calculate denominator: \( -24 - 52=-76 \)
So, \( m=\frac{-40}{-76} \)

Step4: Reduce the fraction

Divide numerator and denominator by their greatest common divisor, which is 4.
\( \frac{-40\div4}{-76\div4}=\frac{-10}{-19}=\frac{10}{19} \)

Answer:

\( \frac{10}{19} \)