Question

write an equation for line l in point - slope form and slope - intercept form.
l is perpendicular to y = 2x.
write an equation for line l in point - slope form.
(simplify your answer. use integers or fractions for any numbers in the equation.)

Explanation:

Step1: Find the slope of line L

The slope of the line \( y = 2x \) is \( m_1 = 2 \). For two perpendicular lines, the product of their slopes is \( -1 \), so if the slope of line L is \( m_2 \), then \( m_1\times m_2=-1 \). Substituting \( m_1 = 2 \), we get \( 2\times m_2=-1 \), so \( m_2 = -\frac{1}{2} \).

Step2: Use the point - slope form formula

The point - slope form of a line is \( y - y_1=m(x - x_1) \), where \( (x_1,y_1) \) is a point on the line and \( m \) is the slope of the line. From the graph, we know that the line L passes through the point \( (-1,-2) \) and has a slope \( m = -\frac{1}{2} \). Substituting \( x_1=-1 \), \( y_1 = - 2 \) and \( m=-\frac{1}{2} \) into the point - slope form formula, we get \( y-(-2)=-\frac{1}{2}(x - (-1)) \), which simplifies to \( y + 2=-\frac{1}{2}(x + 1) \).

Answer:

\( y + 2=-\frac{1}{2}(x + 1) \)