Chapter 4: Q. 348 (page 522)

In the following exercises, use slopes and $y$ -intercepts to determine if the lines are parallel.
$2 x - 4 y = 6; x - 2 y = 3$

Short Answer

Expert verified

The lines are parallel.

Step by step solution

Given information

The given equations are shown below:

$2 x - 4 y = 6 x - 2 y = 3$

Solve the equations for y

Solve $2 x - 4 y = 6$ for $y$ .

$\begin{array}{rcl} - 4 y & = & 6 - 2 x \\ y & = & - \frac{2}{- 4} x + \frac{6}{- 4} \\ y & = & \frac{1}{2} x - \frac{3}{2} \end{array}$

Solve $x - 2 y = 3$ for $y$ .

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

Determine the slope.

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

localid="1648192508377" $m_{1} = \frac{1}{2}, c_{1} = - \frac{3}{2}$

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

localid="1648192519547" $m_{2} = \frac{1}{2}, c_{2} = - \frac{3}{2}$

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

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.
$2 x - 4 y = 6; x - 2 y = 3$

Short Answer

Step by step solution

Given information

Solve the equations for y

Determine the slope.

Write the conclusion

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In the following exercises, use slopes and y-intercepts to determine if the lines are parallel.2x-4y=6;x-2y=3

Short Answer

Step by step solution

Given information

Solve 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

Discrete Mathematics

Pure Maths

Decision Maths

Theoretical and Mathematical Physics

Logic and Functions

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.
$2 x - 4 y = 6; x - 2 y = 3$