Question

find the slope of the line that passes through (-9, 87) and (49, 39). 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, \( x_1=-9 \), \( y_1 = 87 \), \( x_2=49 \), \( y_2=39 \).

Step2: Substitute the values into the formula

Substitute the values into the slope formula: \( m=\frac{39 - 87}{49-(-9)} \).

Step3: Simplify the numerator and the denominator

First, simplify the numerator: \( 39 - 87=-48 \).
Then, simplify the denominator: \( 49-(-9)=49 + 9 = 58 \).
So, \( m=\frac{-48}{58} \).

Step4: Simplify the fraction

We can simplify \( \frac{-48}{58} \) by dividing both the numerator and the denominator by their greatest common divisor, which is 2.
\( \frac{-48\div2}{58\div2}=\frac{-24}{29} \).

Answer:

\( -\frac{24}{29} \)