Question

practice & problem solving
use the figure for exercises 16 - 17. show the
calculations you use to answer each question.

1. are lines p and q parallel?
2. are lines w and t perpendicular?
3. reason theorem 2 - 4 states that two non - vertical lines are perpendicular if and only if the product of their slopes is - 1. why are vertical lines excluded?
4. use structure write an equation for each line that passes through (2, 7) and is parallel or perpendicular to the line y = - 3x - 6.

Explanation:

Step1: Find the slope of line \(p\)

Use the formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\). For line \(p\), if we take two points \((0,1)\) and \((- 1,-2)\), then \(m_p=\frac{-2 - 1}{-1-0}=\frac{-3}{-1}=3\)

Step2: Find the slope of line \(q\)

For line \(q\), if we take two points \((8, - 1)\) and \((6, - 5)\), then \(m_q=\frac{-5+1}{6 - 8}=\frac{-4}{-2}=2\)

Step3: Check if \(m_p=m_q\)

Since \(m_p = 3\) and \(m_q=2\), and \(3
eq2\)

Answer:

Lines \(p\) and \(q\) are not parallel.