Chapter 4, Problem 7CR

To determine

Determine which of the lines ,if any parallel or perpendicular.

Answer to Problem 7CR

Line a and line c is parallel to each other and both are perpendicular to line b.

Explanation of Solution

Given information:

Line a : $2x-7y=14.$

Line b : $y=(7/2)x-8.$

Line c : $2x+7y=-21$ .

Calculation:

Formula :

In general slope intercept equation of a line is,

  $y=mx+b$ ….1

where $m$ is the slope of the line and $b$ is the y-intercept.

Finding $m$:

Slope of line a:

  $\begin{array}{c}2x-7y=14.\\ -7y=14-2x.\\ y=(-2/7)x-2.\end{array}$

So the slope of line a is $m_a=-(2/7)$ .

Slope of line b:

  $y=(7/2)x-8.$

So the slope of line a is $m_b=7/2.$ .

Slope of line c :

  $\begin{array}{c}2x+7y=-21.\\ 7y=-2x-21.\\ y=-(2/7)x-3.\end{array}$

So the slope of line c is $m_c=-(2/7)$ .

So, $m_a=m_c.$

Since the slope of line a is equal to the slope of line c so the line a is parallel to line c because all parallel line have same slope .

Since the slope of two perpendicular lines is negative reciprocal to each other so, line a is perpendicular to line b and line c is also perpendicular to line b because −(2/7) is negative reciprocal to 7/2.

Line a and line c is parallel to each other and both are perpendicular to line b.