Chapter 4.3, Problem 6E

To determine

To calculate: To determine which of the lines are parallel

Answer to Problem 6E

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

Explanation of Solution

Given: Three lines as below:

Line a passes through $\left(-1,3\right)$ and $\left(1,9\right)$

Line b passes through $\left(-2,12\right)$ and $\left(-1,14\right)$

Line a passes through $\left(3,8\right)$ and $\left(6,10\right)$

Formula Used:

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

Slope of line passing through two points given as

  $y=\frac{y_2-y_1}{x_2-x_1}$

Calculation:

Slope of line passing through points $\left(-1,3\right)$ and $\left(1,9\right)$ is calculated as

  $\begin{array}{l}y=\frac{3-9}{-1-1}\\ y=\frac{-6}{-2}\\ y=3\end{array}$

Slope of line passing through points $\left(-2,12\right)$ and $\left(-1,14\right)$ is calculated as

  $\begin{array}{l}y=\frac{14-12}{-1-\left(-2\right)}\\ y=\frac{2}{-1+2}\\ y=-2\end{array}$

Slope of line passing through points $\left(3,8\right)$ and $\left(6,10\right)$ is calculated as

  $\begin{array}{l}y=\frac{10-8}{6-3}\\ y=\frac{2}{-1+2}\\ y=-2\end{array}$

Since the slope of lines $b$ and $c$ are equal

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

Conclusion:

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