Question

line g passes through points (6, 12) and (9, 5). line h passes through points (5, 4) and (2, 11). are line g and line h parallel or perpendicular? parallel perpendicular neither

Explanation:

Step1: Calculate slope of line g

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For line $g$ with points $(x_1,y_1)=(6,12)$ and $(x_2,y_2)=(9,5)$, we have $m_g=\frac{5 - 12}{9 - 6}=\frac{-7}{3}$.

Step2: Calculate slope of line h

For line $h$ with points $(x_1,y_1)=(5,4)$ and $(x_2,y_2)=(2,11)$, we have $m_h=\frac{11 - 4}{2 - 5}=\frac{7}{-3}=-\frac{7}{3}$.

Step3: Check the relationship

Two lines are parallel if their slopes are equal. Since $m_g = m_h=-\frac{7}{3}$, the two lines are parallel.

Answer:

parallel