Question

line v passes through points (9, 9) and (3, 4). line w is parallel to line v. what is the slope of line w? 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 \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Identify points for line v

For line \( v \), \( (x_1, y_1)=(9, 9) \) and \( (x_2, y_2)=(3, 4) \).

Step3: Calculate slope of line v

Substitute into the formula: \( m=\frac{4 - 9}{3 - 9}=\frac{-5}{-6}=\frac{5}{6} \).

Step4: Use parallel lines property

Parallel lines have equal slopes, so slope of \( w \) equals slope of \( v \).

Answer:

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