Chapter 4: Q. 362 (page 522)

In the following exercises, use slopes and $y$ -intercepts to determine if the lines are parallel.
$x - 3 y = 6; 2 x - 6 y = 12$

Short Answer

Expert verified

The lines are parallel.

Step by step solution

Given information

The given equations are shown below:

$x - 3 y = 6 2 x - 6 y = 12$

Solve both the equations for y

Solve $x - 3 y = 6$ for $y$ .

role="math" localid="1648191230920" $\begin{array}{rcl} - 3 y & = & 6 - x \\ y & = & - \frac{x}{- 3} + \frac{6}{- 3} \\ y & = & \frac{1}{3} x - 2 \end{array}$

Solve $2 x - 6 y = 12$ for $y$ .

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

Determine the slope

Compare $\begin{array}{rcl} y & = & \frac{1}{3} x - 2 \end{array}$ with $y = m_{1} x + c_{1}$ .

localid="1648192959804" $m_{1} = \frac{1}{3}, c_{1} = - 2$

Compare $\begin{array}{rcl} y & = & \frac{1}{3} x - 2 \end{array}$ with $y = m_{2} x + c_{2}$ .

localid="1648192968122" $m_{2} = \frac{1}{3}, c_{1} = - 2$

Hence, $m_{1} = m_{2}$

The slope are same and $y$ -intercept are same.

Write the conclusion

The lines are parallel.

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In the following exercises, use slopes and $y$ -intercepts to determine if the lines are parallel.
$x - 3 y = 6; 2 x - 6 y = 12$

Short Answer

Step by step solution

Given information

Solve both the equations for y

Determine the slope

Write the conclusion

One App. One Place for Learning.

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In the following exercises, use slopes and y-intercepts to determine if the lines are parallel.x-3y=6;2x-6y=12

Short Answer

Step by step solution

Given information

Solve both the equations for y

Determine the slope

Write the conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Logic and Functions

Applied Mathematics

Geometry

Statistics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

In the following exercises, use slopes and $y$ -intercepts to determine if the lines are parallel.
$x - 3 y = 6; 2 x - 6 y = 12$