Question

Question 5 of 10
Identify an equation in point-slope form for the line perpendicular to y=-=* + 11 that passes through (4, - 8).
A. y-4=2(2+8)
B. y+8=2（2-4）
C. y - 8 - 4(2 + 4)
D. u - 8 = 6(2 -4)

Answer 1

To find an equation in point-slope form for a line that is perpendicular to the given line and passes through the point (4, -8), we should first identify the slope of the given line, then find the negative reciprocal to use for the perpendicular line.

1. **Identify the slope of the given line:**
The equation provided is in the form of \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. However, your equation appears to be missing some details with the "=-*". Assuming it is meant to be a linear equation:

Let's say the equation is \( y = mx + 11 \).

Without the exact equation, let's say the slope (\( m \)) of the line is \( m = -\frac{1}{2} \) (this is just an example, as the slope is not clearly mentioned).

2. **Find the slope of the perpendicular line:**
The slope of a line that is perpendicular to another is the negative reciprocal of the original slope. If the slope of the original line is \( m = -\frac{1}{2} \), the slope of the perpendicular line will be \( m_{\perpendicular} = 2 \).

3. **Use the point-slope form:**
The point-slope form is given by the equation:
\[
y - y_1 = m(x - x_1)
\]
where \( (x_1, y_1) \) is a point on the line (which is (4, -8) in this case) and \( m \) is the slope we found (2).

Plugging these values into the point-slope equation gives:
\[
y - (-8) = 2(x - 4)
\]
Simplifying this yields:
\[
y + 8 = 2(x - 4)
\]

4. **Check the options:**
A. \( y - 4 = 2(2 + 8) \) - Incorrect format and values.

B. \( y + 8 = 2(x - 4) \) - This is the correct equation.

C. \( y - 8 - 4(2 + 4) \) - Incorrect and does not match the point-slope form.

D. \( y - 8 = 6(2 - 4) \) - Incorrect and does not match the right format or values.

Thus, the correct answer is:
**B. \( y + 8 = 2(x - 4) \)**.