Question

Select the correct answer.
Which equation represents the line that is perpendicular to y - 3/2x+ 1
and passes through (-12,6)?
A. y = -2/3x -16
B. y = -2/3x - 2
C. y = 3/2x - 21
D. y = 3/2x + 24

Answer 1

To find the line that is perpendicular to the given line \( y - \frac{3}{2}x + 1 \) and passes through the point (-12, 6), we need to follow these steps:

1. **Identify the slope of the given line**: The equation can be rewritten in slope-intercept form:
\[
y = \frac{3}{2}x - 1
\]
Hence, the slope (m) of the given line is \( \frac{3}{2} \).

2. **Determine the slope of the perpendicular line**: The slope of a line that is perpendicular to another line is the negative reciprocal of the original slope. Therefore, the slope of the perpendicular line is:
\[
m_{\text{perpendicular}} = -\frac{1}{\frac{3}{2}} = -\frac{2}{3}
\]

3. **Use the point-slope form of the equation to find the line**: We use the point-slope form, \( y - y_1 = m(x - x_1) \), where \( (x_1, y_1) = (-12, 6) \) and \( m = -\frac{2}{3} \).
\[
y - 6 = -\frac{2}{3}(x + 12)
\]

4. **Simplifying the equation**:
\[
y - 6 = -\frac{2}{3}x - 8
\]
\[
y = -\frac{2}{3}x - 2
\]

Now we can compare our final equation \( y = -\frac{2}{3}x - 2 \) to the provided options:

**The correct answer is:**
B. \( y = -\frac{2}{3}x - 2 \)