Question

topic: parallel and perpendicular lines
progress:
the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer.
find the equation of the line that contains the point (6, -2) and is perpendicular to the line y = -2x + 8.
y = 2x - 14
y = \frac{1}{2}x - 5
y = -\frac{1}{2}x
y = -2x + 10

Explanation:

Step1: Identify slope of given line

The given line is \( y = -2x + 8 \), so its slope \( m_1 = -2 \).

Step2: Find perpendicular slope

Perpendicular slopes multiply to -1: \( m_2 = \frac{1}{2} \) (since \( -2 \times \frac{1}{2} = -1 \)).

Step3: Use point-slope form

Point-slope formula: \( y - y_1 = m(x - x_1) \). Substitute \( (6, -2) \) and \( m = \frac{1}{2} \):
\( y - (-2) = \frac{1}{2}(x - 6) \)
Simplify: \( y + 2 = \frac{1}{2}x - 3 \) → \( y = \frac{1}{2}x - 5 \).

Answer:

B. \( y = \frac{1}{2}x - 5 \)