Chapter 4.3, Problem 11Q

To determine

To calculate: To determine which of the lines are parallel or perpendicular

Answer to Problem 11Q

Theline $c$ and line $b$ are parallel.

Explanation of Solution

Given: Equation of three lines as below:

Line a $:2x+6y=-12$

Line b $:y=\frac{3}{2}x-5$

Line c $:3x-2y=-4$

Formula Used:

When two lines are parallel, then the slopes of lines are equal

Calculation:

Equation of linea $:2x+6y=-12$

  $\begin{array}{l}2x+6y=-12\\ 6y=-2x-12\\ y=-\frac{1}{3}x-2\end{array}$

Comparing the above equation with slope intercept form of line:

  $m=-\frac{1}{3}$

Equation of lineb $:y=\frac{3}{2}x-5$

Comparing the above equation with slope intercept form of line:

  $m=\frac{3}{2}$

Equation of linec $:3x-2y=-4$

  $\begin{array}{l}3x-2y=-4\\ 2y=3x+4\\ y=\frac{3}{2}x+2\end{array}$

Comparing the above equation with slope intercept form of line:

  $m=\frac{3}{2}$

Since the slopes of line $c$ and line $b$ are equal

Thus, line $c$ and line $b$ are parallel.

Conclusion:

Hence, line $a$ and line $c$ are parallel.