Question

line u passes through points (10, 9) and (7, 4). line v is parallel to line u. what is the slope of line v? 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 u

For line u, \( (x_1, y_1) = (10, 9) \) and \( (x_2, y_2) = (7, 4) \).

Step3: Calculate slope of line u

Substitute into the formula: \( m = \frac{4 - 9}{7 - 10} = \frac{-5}{-3} = \frac{5}{3} \).

Step4: Use parallel lines property

Parallel lines have equal slopes, so slope of line v is equal to slope of line u.

Answer:

\(\frac{5}{3}\)