Chapter 4.3, Problem 4E

To determine

To calculate: To determine which of the lines are parallel

Answer to Problem 4E

Thelines passing through points $\left(3,4\right),\left(5,0\right)$ and $\left(4,6\right),\left(5,4\right)$ are parallel.

Explanation of Solution

Given: Graph of lines is

  

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:

Graph of lines is given as

  

Slope of line passing through points $\left(0,5\right),\left(2,0\right)$ is calculated as

  $\begin{array}{l}y=\frac{0-5}{2-0}\\ y=-\frac{5}{2}\end{array}$

Slope of line passing through points $\left(3,4\right),\left(5,0\right)$ is calculated as

  $\begin{array}{l}y=\frac{4-0}{3-5}\\ y=\frac{4}{-2}\\ y=-2\end{array}$

Slope of line passing through points $\left(4,6\right),\left(5,4\right)$ is calculated as

  $\begin{array}{l}y=\frac{6-4}{4-5}\\ y=\frac{2}{-1}\\ y=-2\end{array}$

Since the slope of lines passing through points $\left(3,4\right),\left(5,0\right)$ and $\left(4,6\right),\left(5,4\right)$ are equal.

Thus, the above lines are parallel.

Conclusion:

Hence, lines passing through points $\left(3,4\right),\left(5,0\right)$ and $\left(4,6\right),\left(5,4\right)$ are parallel.