Chapter 3.4, Problem 47PPS

To determine

To determine whether lines are parallel, perpendicular or neither.

  $y=-\frac{1}{2}x-12$

  $y=2x+7$

Answer to Problem 47PPS

Lines are perpendicular.

Explanation of Solution

Given information:

Lines

  $y=-\frac{1}{2}x-12$

  $y=2x+7$

Formula used:

For parallel lines

  $m_1=m_2$

For perpendicular lines

  $m_1\times m_2=-1$

Calculation:

Line 1

  $y=-\frac{1}{2}x-12$

Then slope of line 1

  $m_1=-\frac{1}{2}$

Line 2

  $y=2x+7$

Then slope of line 2

  $m_2=2$

Here

  $m_1\ne m_2$

Then check for perpenticular

Using perperdicular lines formula

  $m_1\times m_2=-1$

Substitute values of slopes

  $-\frac{1}{2}\times 2=-1$

On solving

  $-1=-1$

Hence, lines are perpendicular.