Question

find an equation of the line l
l is perpendicular to y = -2x
the equation is
(type an equation. use integers or fractions for any numbers in the equation. simplify your answer.)

Explanation:

Step1: Find slope of perpendicular line

The slope of \( y = -2x \) is \( m_1 = -2 \). For perpendicular lines, \( m_1 \times m_2 = -1 \), so \( -2 \times m_2 = -1 \Rightarrow m_2 = \frac{1}{2} \).

Step2: Use point - slope form

Line \( L \) passes through \( (3, -6) \). Point - slope form: \( y - y_1 = m(x - x_1) \), where \( x_1 = 3 \), \( y_1 = -6 \), \( m=\frac{1}{2} \).
Substitute: \( y - (-6)=\frac{1}{2}(x - 3) \)

Step3: Simplify the equation

\( y + 6=\frac{1}{2}x-\frac{3}{2} \)
Subtract 6 (or \( \frac{12}{2} \)) from both sides: \( y=\frac{1}{2}x-\frac{3}{2}-\frac{12}{2}=\frac{1}{2}x-\frac{15}{2} \)
Multiply both sides by 2 to eliminate fractions: \( 2y=x - 15 \), or \( x - 2y = 15 \), or \( y=\frac{1}{2}x-\frac{15}{2} \) (any simplified form is acceptable, but let's check with the point: when \( x = 3 \), \( y=\frac{1}{2}(3)-\frac{15}{2}=\frac{3 - 15}{2}=-6 \), which matches the point \( (3,-6) \))

Answer:

\( y=\frac{1}{2}x-\frac{15}{2} \) (or equivalent forms like \( x - 2y = 15 \))