Question

find the slope of the line that passes through (25, 37) and (-33, -9). 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, \( (x_1, y_1)=(25, 37) \) and \( (x_2, y_2)=(- 33,-9) \).

Step2: Substitute the values into the formula

Substitute \( x_1 = 25,y_1 = 37,x_2=-33,y_2=-9 \) into the slope formula:
\( m=\frac{-9 - 37}{-33 - 25} \)

Step3: Simplify the numerator and the denominator

First, simplify the numerator: \( -9-37=-46 \)
Then, simplify the denominator: \( -33 - 25=-58 \)
So, \( m=\frac{-46}{-58} \)

Step4: Reduce the fraction

We can divide both the numerator and the denominator by their greatest common divisor, which is 2.
\( \frac{-46\div2}{-58\div2}=\frac{23}{29} \)

Answer:

\( \frac{23}{29} \)