Chapter 4: Q. 368 (page 522)

In the following exercises, use slopes and $y$ -intercepts to determine if the lines are parallel.
$7 x - 4 y = 8; 4 x + 7 y = 14$

Short Answer

Expert verified

The lines are not parallel.

Step by step solution

Given information

The given equations are shown below:

$7 x - 4 y = 8 4 x + 7 y = 14$

Solve both the equations for y

Solve $7 x - 4 y = 8$ for $y$ .

$\begin{array}{rcl} - 4 y & = & 8 - 7 x \\ y & = & - \frac{7 x}{- 4} + \frac{8}{- 4} \\ y & = & \frac{7}{4} x - 2 \end{array}$

Solve $4 x + 7 y = 14$ for $y$ .

$\begin{array}{rcl} 7 y & = & 14 - 4 x \\ y & = & - \frac{4 x}{7} + \frac{14}{7} \\ y & = & - \frac{4}{7} x + 2 \end{array}$

Determine the slope

Compare $\begin{array}{rcl} y & = & \frac{7}{4} x - 2 \end{array}$ with $y = m_{1} x + c_{1}$ .

$m_{1} = \frac{7}{4}, c_{1} = - 2$

Compare $\begin{array}{rcl} y & = & - \frac{4}{7} x + 2 \end{array}$ with $y = m_{2} x + c_{2}$ .

$m_{2} = - \frac{4}{7}, c_{2} = 2$

Here, $m_{1} \neq m_{2}$ .

The slopes are different and $y$ -intercept are different.

Write the conclusion

The lines are not parallel.

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In the following exercises, use slopes and $y$ -intercepts to determine if the lines are parallel.
$7 x - 4 y = 8; 4 x + 7 y = 14$

Short Answer

Step by step solution

Given information

Solve both 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.7x-4y=8;4x+7y=14

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

Discrete Mathematics

Logic and Functions

Statistics

Calculus

Theoretical and Mathematical Physics

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.
$7 x - 4 y = 8; 4 x + 7 y = 14$