Question

find the slope of the line that passes through (49, -3) and (13, -33). 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, \( x_1 = 49 \), \( y_1=-3 \), \( x_2 = 13 \), and \( y_2=-33 \).

Step2: Substitute the values into the formula

Substitute the values into the slope formula: \( m=\frac{-33-(-3)}{13 - 49} \).
Simplify the numerator and the denominator:
The numerator: \( -33-(-3)=-33 + 3=-30 \).
The denominator: \( 13 - 49=-36 \).
So, \( m=\frac{-30}{-36} \).

Step3: Simplify the fraction

Simplify \( \frac{-30}{-36} \) by dividing both the numerator and the denominator by their greatest common divisor, which is 6.
\( \frac{-30\div6}{-36\div6}=\frac{5}{6} \).

Answer:

\( \frac{5}{6} \)