Question

Given y, equals, minus, start fraction, 2, divided by, 3, end fraction, x, minus, 6, .y=−
3
2
​
x−6
Answer
Attempt 1 out of 100

Parallel slope (m, start subscript, vertical bar, vertical bar, end subscriptm
∣∣
​
)=
.
Perpendicular slope (m, start subscript, is perpendicular to, end subscriptm
⊥
​
)=

Answer 1

The equation you provided is:

\[ y = -\frac{2}{3} x - 6 \]

The slope (m) of this line is given by the coefficient of X, which is \(-\frac{2}{3}\).

### To find the parallel and perpendicular slopes:

1. **Parallel slope (m∣)**: Two lines that are parallel have the same slope. Thus, the parallel slope is:

\[
m∣ = -\frac{2}{3}
\]

2. **Perpendicular slope (m⊥)**: Two lines are perpendicular if the product of their slopes is \(-1\). To find the slope of a line that is perpendicular to the given slope \(-\frac{2}{3}\), you can take the negative reciprocal:

\[
m⊥ = -\frac{1}{m} = -\frac{1}{-\frac{2}{3}} = \frac{3}{2}
\]

### Summary of Results:
- Parallel slope (m∣) = \(-\frac{2}{3}\)
- Perpendicular slope (m⊥) = \(\frac{3}{2}\)