Question

find the slope of the line that passes through (7, 6) and (5, 5). 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 \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Here, \( (x_1,y_1)=(7,6) \) and \( (x_2,y_2)=(5,5) \).

Step2: Substitute values

Substitute \( x_1 = 7 \), \( y_1 = 6 \), \( x_2 = 5 \), \( y_2 = 5 \) into the formula: \( m=\frac{5 - 6}{5 - 7} \).

Step3: Simplify numerator and denominator

Simplify numerator: \( 5 - 6=-1 \). Simplify denominator: \( 5 - 7=-2 \). So \( m=\frac{-1}{-2} \).

Step4: Reduce the fraction

\( \frac{-1}{-2}=\frac{1}{2} \).

Answer:

\(\frac{1}{2}\)