Question

line g passes through points (56, 31) and (70, 100). line h is parallel to line g. what is the slope of line h? 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 g

For line \( g \), \( x_1 = 56 \), \( y_1 = 31 \), \( x_2 = 70 \), \( y_2 = 100 \).

Step3: Calculate slope of line g

Substitute into the formula: \( m=\frac{100 - 31}{70 - 56}=\frac{69}{14} \).

Step4: Use parallel lines property

Parallel lines have equal slopes, so slope of line \( h \) equals slope of line \( g \).

Answer:

\(\frac{69}{14}\)