Question

line g has an equation of y = 2x + 1. line h includes the point (-5, 2) and is perpendicular to line g. what is the equation of line h?
write the equation in slope - intercept form. write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

Explanation:

Step1: Find slope of line g

Line g: \( y = 2x + 1 \), slope \( m_g = 2 \).

Step2: Find slope of line h

Perpendicular slopes: \( m_g \times m_h = -1 \), so \( 2 \times m_h = -1 \), \( m_h = -\frac{1}{2} \).

Step3: Use point - slope form

Point \((-5, 2)\), point - slope: \( y - y_1 = m(x - x_1) \), so \( y - 2 = -\frac{1}{2}(x + 5) \).

Step4: Convert to slope - intercept

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

Answer:

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