Question

1. write the equation that is perpendicular to $y = -3x + 2$ and passes through the point $(9, -1)$

Explanation:

Step1: Find the slope of the perpendicular line

The slope of the given line \( y = -3x + 2 \) is \( m_1=-3 \). For two perpendicular lines, the product of their slopes is \( -1 \), i.e., \( m_1\times m_2=-1 \). So, \( -3\times m_2=-1 \), which gives \( m_2=\frac{1}{3} \).

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 \( (x_1,y_1)=(9,-1) \) and \( m = \frac{1}{3} \). Substituting these values, we get \( y-(-1)=\frac{1}{3}(x - 9) \).

Step3: Simplify the equation

Simplify \( y + 1=\frac{1}{3}x-3 \). Subtract 1 from both sides: \( y=\frac{1}{3}x-3 - 1 \), so \( y=\frac{1}{3}x-4 \).

Answer:

\( y=\frac{1}{3}x - 4 \)