Question

write the equation of a line that is perpendicular to $y = 3x - 2$ and that passes through the point $(-9, 5)$.

Explanation:

Step1: Find the slope of the perpendicular line

The slope of the given line \( y = 3x - 2 \) is \( m = 3 \). The slope of a line perpendicular to it is the negative reciprocal, so \( m_{\perp}=-\frac{1}{3} \).

Step2: Use point - slope form to find the equation

The point - slope form of a line is \( y - y_1=m(x - x_1) \), where \( (x_1,y_1)=(-9,5) \) and \( m = -\frac{1}{3} \).
Substitute the values: \( y - 5=-\frac{1}{3}(x + 9) \)
Simplify: \( y - 5=-\frac{1}{3}x-3 \)
Add 5 to both sides: \( y=-\frac{1}{3}x + 2 \)

Answer:

\( y = -\frac{1}{3}x+2 \)