**Title: Classifying Pairs of Lines as Parallel, Perpendicular, or Neither**---**Instruction:**The following pairs of lines are either parallel, perpendicular, or neither. Move each pair of lines to the correct column.---**Categories:**- **Parallel** - No Answers Chosen- **Perpendicular** - No Answers Chosen- **Neither parallel nor perpendicular** - No Answers Chosen---**Possible Answers:**1. $ 5x - 3y = 18 $ and $ 6x + 10y = 4 $2. $ x - 5y = 20 $ and $ 10x - 4y = -20 $3. $ -3x + y = 16 $ and $ 9x - 3y = 11 $4. $ 4x + 6y = 10 $ and $ 3x + 2y = -8 $---**How to Determine:**1. **Parallel Lines:** - If two lines are parallel, they have the same slope (i.e., their coefficients of $x$ and $y$ are proportional). 2. **Perpendicular Lines:** - If two lines are perpendicular, the product of their slopes is $-1$ (i.e., if the slope of one line is $m$, the slope of the other line should be $-\frac{1}{m}$). 3. **Neither:** - If the lines are neither parallel nor perpendicular, they do not satisfy the conditions for either parallel or perpendicular lines.For each pair of lines, convert the equations to their slope-intercept form ($y = mx + b$) to find the slopes and then classify them accordingly.

The equation is called the linear equation in two variables. Here, the variables are x and y. The…

The following pairs of lines are either parallel, perpendicular, or neither. Move each pair of lines to the correct column. Parallel Perpendicular No Answers Chosen No Answers Chosen Neither parallel nor perpendicular No Answers Chosen Possible answvers ! 5x-3y - 18 and 6x + 10y -4 I x-5y - 20 and 10x-4y--20 ! -3x +y= 16 and 9x -3y = 11 | 4x+ 6y -10 and 3x+2y =-8 %3!

The following pairs of lines are either parallel, perpendicular, or neither. Move each pair of lines to the correct column. Parallel Perpendicular No Answers Chosen No Answers Chosen Neither parallel nor perpendicular No Answers Chosen Possible answvers ! 5x-3y - 18 and 6x + 10y -4 I x-5y - 20 and 10x-4y--20 ! -3x +y= 16 and 9x -3y = 11 | 4x+ 6y -10 and 3x+2y =-8 %3!

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Question

**Title: Classifying Pairs of Lines as Parallel, Perpendicular, or Neither**

---

**Instruction:**
The following pairs of lines are either parallel, perpendicular, or neither. Move each pair of lines to the correct column.

---

**Categories:**

- **Parallel**
- No Answers Chosen

- **Perpendicular**
- No Answers Chosen

- **Neither parallel nor perpendicular**
- No Answers Chosen

---

**Possible Answers:**

1. $ 5x - 3y = 18 $ and $ 6x + 10y = 4 $
2. $ x - 5y = 20 $ and $ 10x - 4y = -20 $
3. $ -3x + y = 16 $ and $ 9x - 3y = 11 $
4. $ 4x + 6y = 10 $ and $ 3x + 2y = -8 $

---

**How to Determine:**

1. **Parallel Lines:**
- If two lines are parallel, they have the same slope (i.e., their coefficients of $x$ and $y$ are proportional).

2. **Perpendicular Lines:**
- If two lines are perpendicular, the product of their slopes is $-1$ (i.e., if the slope of one line is $m$, the slope of the other line should be $-\frac{1}{m}$).

3. **Neither:**
- If the lines are neither parallel nor perpendicular, they do not satisfy the conditions for either parallel or perpendicular lines.

For each pair of lines, convert the equations to their slope-intercept form ($y = mx + b$) to find the slopes and then classify them accordingly.

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