Answered

Discover a world of knowledge and community-driven answers at IDNLearn.com today. Ask your questions and receive accurate, in-depth answers from our knowledgeable community members.

Drag the tiles to the correct boxes to complete the pairs. Determine whether each pair of lines is perpendicular, parallel, or neither.

[tex]\[
\begin{array}{ccc}
\hline
y = 2x + 4 & 4y = 2x - 4 & 2y = 4x + 4 \\
2y = 4x - 7 & y = -2x + 9 & y = -2x - 2 \\
\hline
\end{array}
\][/tex]

Neither [tex]$\square$[/tex] [tex]\(\square\)[/tex] [tex]\(\square\)[/tex]
Parallel [tex]$\square$[/tex] [tex]\(\square\)[/tex]

Sagot :

GinnyAnsweridn
Let's work step-by-step to determine the relationships between each pair of given lines based on their slopes.

1. Pair: [tex]\( y=2x+4 \)[/tex] and [tex]\( 4y=2x-4 \)[/tex]
- Rewriting [tex]\( 4y=2x-4 \)[/tex] in slope-intercept form:
[tex]\[ 4y = 2x - 4 \implies y = \frac{1}{2}x - 1 \][/tex]
- The slopes are 2 and [tex]\(\frac{1}{2}\)[/tex]. The slopes are not equal and their product is not [tex]\(-1\)[/tex], so the lines are neither parallel nor perpendicular.

2. Pair: [tex]\( 4y=2x-4 \)[/tex] and [tex]\( 2y=4x-7 \)[/tex]
- Rewriting [tex]\( 2y=4x-7 \)[/tex]:
[tex]\[ 2y = 4x - 7 \implies y = 2x - \frac{7}{2} \][/tex]
- The slopes are [tex]\(\frac{1}{2}\)[/tex] and 2. The slopes are not equal and their product is not [tex]\(-1\)[/tex], so the lines are neither parallel nor perpendicular.

3. Pair: [tex]\( 2y=4x-7 \)[/tex] and [tex]\( y=-2x+9 \)[/tex]
- The slopes are 2 and -2. The slopes are not equal and their product is not [tex]\(-1\)[/tex], so the lines are neither parallel nor perpendicular.

4. Pair: [tex]\( y=-2x+9 \)[/tex] and [tex]\( y=-2x-2 \)[/tex]
- The slopes are both -2. The slopes are equal, so the lines are parallel.

5. Pair: [tex]\( y=-2x-2 \)[/tex] and [tex]\( 2y=4x+4 \)[/tex]
- Rewriting [tex]\( 2y=4x+4 \)[/tex] in slope-intercept form:
[tex]\[ 2y = 4x + 4 \implies y = 2x + 2 \][/tex]
- The slopes are -2 and 2. The slopes are not equal and their product is not [tex]\(-1\)[/tex], so the lines are neither parallel nor perpendicular.

6. Pair: [tex]\( 2y=4x+4 \)[/tex] and [tex]\( y=2x+4 \)[/tex]
- The slopes are both 2. The slopes are equal, so the lines are parallel.

Now, let's organize the pairs based on the determined relationships:

### Neither
- [tex]\( y=2x+4 \)[/tex] and [tex]\( 4y=2x-4 \)[/tex]
- [tex]\( 4y=2x-4 \)[/tex] and [tex]\( 2y=4x-7 \)[/tex]
- [tex]\( 2y=4x-7 \)[/tex] and [tex]\( y=-2x+9 \)[/tex]
- [tex]\( y=-2x-2 \)[/tex] and [tex]\( 2y=4x+4 \)[/tex]

### Parallel
- [tex]\( y=-2x+9 \)[/tex] and [tex]\( y=-2x-2 \)[/tex]
- [tex]\( 2y=4x+4 \)[/tex] and [tex]\( y=2x+4 \)[/tex]

Therefore, the pairs are arranged as follows:

Neither
- [tex]\( y=2x+4 \)[/tex] and [tex]\( 4y=2x-4 \)[/tex]
- [tex]\( 4y=2x-4 \)[/tex] and [tex]\( 2y=4x-7 \)[/tex]
- [tex]\( 2y=4x-7 \)[/tex] and [tex]\( y=-2x+9 \)[/tex]
- [tex]\( y=-2x-2 \)[/tex] and [tex]\( 2y=4x+4 \)[/tex]

Parallel
- [tex]\( y=-2x+9 \)[/tex] and [tex]\( y=-2x-2 \)[/tex]
- [tex]\( 2y=4x+4 \)[/tex] and [tex]\( y=2x+4 \)[/tex]
We value your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. Your questions find answers at IDNLearn.com. Thanks for visiting, and come back for more accurate and reliable solutions.