Question

1. write an equation of the line that passes through (6, -9) and is perpendicular to the line ( y = -\frac{3}{8}x + 1 ). an equation of the perpendicular line is ( y = square ).

Explanation:

Step1: Find the slope of the perpendicular line

The given line is \( y = -\frac{3}{8}x + 1 \), so its slope \( m_1 = -\frac{3}{8} \). The slope of a line perpendicular to it, \( m_2 \), satisfies \( m_1 \times m_2 = -1 \). So \( -\frac{3}{8} \times m_2 = -1 \), solving for \( m_2 \) gives \( m_2 = \frac{8}{3} \).

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 \( (x_1,y_1)=(6, - 9) \) and \( m=\frac{8}{3} \). Substituting these values, we get \( y - (-9)=\frac{8}{3}(x - 6) \).

Step3: Simplify the equation

\( y + 9=\frac{8}{3}x-16 \). Subtract 9 from both sides: \( y=\frac{8}{3}x-16 - 9 \), so \( y=\frac{8}{3}x-25 \).

Answer:

\( \frac{8}{3}x - 25 \)