Question

line p passes through points (8, 5) and (1, 10). line q passes through points (8, 10) and (1, 15). are line p and line q parallel or perpendicular? parallel perpendicular neither save answer

Explanation:

Step1: Calculate slope of line p

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. For line $p$ with points $(8,5)$ and $(1,10)$, we have $m_p=\frac{10 - 5}{1 - 8}=\frac{5}{-7}=-\frac{5}{7}$.

Step2: Calculate slope of line q

For line $q$ with points $(8,10)$ and $(1,15)$, using the slope formula $m = \frac{y_2 - y_1}{x_2 - x_1}$, we get $m_q=\frac{15 - 10}{1 - 8}=\frac{5}{-7}=-\frac{5}{7}$.

Step3: Determine relationship

Parallel lines have equal slopes. Since $m_p = m_q=-\frac{5}{7}$, the lines are parallel.

Answer:

parallel