Chapter 4: Q. 351 (page 522)

In the following exercises, use slopes and $y$ -intercepts to determine if the lines are parallel.
$8 x + 6 y = 6; 12 x + 9 y = 12$

Short Answer

Expert verified

The lines are parallel.

Step by step solution

Given information

The given equations are shown below:

$8 x + 6 y = 6 12 x + 9 y = 12$

Solve both the equation for y

Solve $8 x + 6 y = 6$ for $y$ .

$\begin{array}{rcl} 6 y & = & 6 - 8 x \\ y & = & - \frac{8}{6} x + \frac{6}{6} \\ y & = & - \frac{4}{3} x + 1 \end{array}$

Solve $12 x + 9 y = 12$ for $y$ .

$\begin{array}{rcl} 9 y & = & 12 - 12 x \\ y & = & - \frac{12}{9} x + \frac{12}{9} \\ y & = & - \frac{4}{3} x + \frac{4}{3} \end{array}$

Determine the slope.

Compare $\begin{array}{rcl} y & = & - \frac{4}{3} x + 1 \end{array}$ with $y = m_{1} x + c_{1}$ .

localid="1648192689396" $m_{1} = - \frac{4}{3}, c_{1} = 1$

Compare $\begin{array}{rcl} y & = & - \frac{4}{3} x + \frac{4}{3} \end{array}$ with $y = m_{2} x + c_{2}$ .

localid="1648192698624" $m_{2} = - \frac{4}{3}, c_{2} = \frac{4}{3}$

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

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

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.
$8 x + 6 y = 6; 12 x + 9 y = 12$

Short Answer

Step by step solution

Given information

Solve both the equation 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.8x+6y=6;12x+9y=12

Short Answer

Step by step solution

Given information

Solve both the equation 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

Logic and Functions

Mechanics Maths

Discrete Mathematics

Theoretical and Mathematical Physics

Applied Mathematics

Decision Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, use slopes and $y$ -intercepts to determine if the lines are parallel.
$8 x + 6 y = 6; 12 x + 9 y = 12$