Question

Are the pairs of lines parallel, perpendicular, or intersecting?(3 points)
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y−6=14(x+2)

y=−4x−10

2x−y=7

3x−4y=−8

y=−23x+7

−2x−3y=12
answers
parellel, perpendiculer, intersecting

Answer 1

Let's analyze the given lines to determine if they are parallel, perpendicular, or intersecting.

1. **Line 1**: \( y - 6 = 14(x + 2) \)
- Rearranging to slope-intercept form (y = mx + b):
\[
y - 6 = 14x + 28 \implies y = 14x + 34
\]
- Slope (m) = 14

2. **Line 2**: \( y = -4x - 10 \)
- Slope (m) = -4

3. **Line 3**: \( 2x - y = 7 \)
- Rearranging to slope-intercept form:
\[
-y = -2x + 7 \implies y = 2x - 7
\]
- Slope (m) = 2

4. **Line 4**: \( 3x - 4y = -8 \)
- Rearranging to slope-intercept form:
\[
-4y = -3x - 8 \implies y = \frac{3}{4}x + 2
\]
- Slope (m) = \(\frac{3}{4}\)

5. **Line 5**: \( y = -23x + 7 \)
- Slope (m) = -23

6. **Line 6**: \( -2x - 3y = 12 \)
- Rearranging to slope-intercept form:
\[
-3y = 2x + 12 \implies y = -\frac{2}{3}x - 4
\]
- Slope (m) = -\(\frac{2}{3}\)

Now, let's compare the slopes to determine relationships:

- **Line 1 (Slope 14)** and **Line 2 (Slope -4)**: Not equal and not negative reciprocals, so they are **intersecting**.
- **Line 1 (Slope 14)** and **Line 3 (Slope 2)**: Not equal and not negative reciprocals, so they are **intersecting**.
- **Line 1 (Slope 14)** and **Line 4 (Slope 3/4)**: Not equal and not negative reciprocals, so they are **intersecting**.
- **Line 1 (Slope 14)** and **Line 5 (Slope -23)**: Not equal and not negative reciprocals, so they are **intersecting**.
- **Line 1 (Slope 14)** and **Line 6 (Slope -2/3)**: Not equal and not negative reciprocals, so they are **intersecting**.

- **Line 2 (Slope -4)** and **Line 3 (Slope 2)**: Not equal and not negative reciprocals, so they are **intersecting**.
- **Line 2 (Slope -4)** and **Line 4 (Slope 3/4)**: Not equal and not negative reciprocals, so they are **intersecting**.
- **Line 2 (Slope -4)** and **Line 5 (Slope -23)**: Not equal and not negative reciprocals, so they are **intersecting**.
- **Line 2 (Slope -4)** and **Line 6 (Slope -2/3)**: Not equal and not negative reciprocals, so they are **intersecting**.

- **Line 3 (Slope 2)** and **Line 4 (Slope 3/4)**: Not equal and not negative reciprocals, so they are **intersecting**.
- **Line 3 (Slope 2)** and **Line 5 (Slope -23)**: Not equal and not negative reciprocals, so they are **intersecting**.
- **Line 3 (Slope 2)** and **Line 6 (Slope -2/3)**: Not equal and not negative reciprocals, so they are **intersecting**.

- **Line 4 (Slope 3/4)** and **Line 5 (Slope -23)**: Not equal and not negative reciprocals, so they are **intersecting**.
- **Line 4 (Slope 3/4)** and **Line 6 (Slope -2/3)**: Not equal and not negative reciprocals, so they are **intersecting**.

- **Line 5 (Slope -23)** and **Line 6 (Slope -2/3)**: Not equal and not negative reciprocals, so they are **intersecting**.

In conclusion, all pairs of lines are **intersecting**. You can select "intersecting" for all pairs.