Question

Line a is represented by the equation y=3x−4.

How do these equations compare to line a?

Drag and drop the equations into the boxes to complete the table.

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Parallel to line a Perpendicular to line a Neither parallel nor perpendicular to line a


A. y = - 1/3 x - 10
B. y = 1/3 x + 1
C. y = 3x - 2

Answer 1

To determine how the given equations compare to line a (y = 3x - 4), we need to analyze the slopes of each line.

1. **Line a has a slope of 3.**
2. **Parallel lines** have the same slope.
3. **Perpendicular lines** have slopes that are negative reciprocals of each other (the product of their slopes equals -1).

Now, let's analyze each equation:

**A. y = -1/3 x - 10**
- Slope = -1/3
- This slope is neither equal to 3 (not parallel) nor the negative reciprocal of 3 (not perpendicular).
- **Category: Neither parallel nor perpendicular to line a**

**B. y = 1/3 x + 1**
- Slope = 1/3
- This slope is not equal to 3 (not parallel) and it's not the negative reciprocal of 3 (not perpendicular).
- **Category: Neither parallel nor perpendicular to line a**

**C. y = 3x - 2**
- Slope = 3
- This slope is equal to 3 (parallel).
- **Category: Parallel to line a**

Here’s how you would arrange them in the table:
- Parallel to line a: **C. y = 3x - 2**
- Perpendicular to line a: (none)
- Neither parallel nor perpendicular to line a: **A. y = -1/3 x - 10** and **B. y = 1/3 x + 1**