Question

find the slope of the line that passes through (3, 4) and (7, 1). 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, \( (x_1, y_1)=(3, 4) \) and \( (x_2, y_2)=(7, 1) \).

Step2: Substitute the values into the formula

Substitute \( x_1 = 3 \), \( y_1 = 4 \), \( x_2 = 7 \), and \( y_2 = 1 \) into the slope formula:
\( m=\frac{1 - 4}{7 - 3} \)

Step3: Simplify the numerator and the denominator

Simplify the numerator: \( 1-4=-3 \)
Simplify the denominator: \( 7 - 3 = 4 \)
So, \( m=\frac{-3}{4}=-\frac{3}{4} \)

Answer:

\(-\frac{3}{4}\)