Question

Select the TWO lines from this list that are perpendicular. (1 point)

y-2=(x+1)

4z3y-6

5x-3y-3

y=-x+12

Answer 1

To determine which lines are perpendicular, we need to find their slopes. Lines are perpendicular if the product of their slopes is -1.

Let's analyze the lines provided:

1. **y - 2 = (x + 1)**:
Rearranging to slope-intercept form (y = mx + b):
\[
y = x + 3
\]
The slope (m) is 1.

2. **4z3y - 6**:
This line is not in a recognizable form for analyzing a slope and seems like a typo or an invalid expression.

3. **5x - 3y - 3 = 0**:
Rearranging to slope-intercept form:
\[
3y = 5x - 3 \implies y = \frac{5}{3}x - 1
\]
The slope (m) is \(\frac{5}{3}\).

4. **y = -x + 12**:
This is already in slope-intercept form:
The slope (m) is -1.

Now we can look for pairs of slopes that multiply to -1:
- **Line 1**: Slope = 1
- **Line 3**: Slope = \(\frac{5}{3}\)
- **Line 4**: Slope = -1

Checking the slopes:
- Slope of Line 1 (1) and Slope of Line 4 (-1): \(1 \times -1 = -1\) ✔️
- Other pairs do not multiply to -1.

Thus, the two lines that are perpendicular are:
- Line 1: \(y - 2 = (x + 1)\) (or \(y = x + 3\))
- Line 4: \(y = -x + 12\)

So, the correct answer is:
**Line 1: y - 2 = (x + 1)** and **Line 4: y = -x + 12**.