the equation of line v is y = 9x + 1. line w is perpendicular to line v and passes through (3, -2). what is…

Explanation:

Step1: Find the slope of line w

The slope of line v is $m_v = 9$. For two perpendicular lines, the product of their slopes is - 1. Let the slope of line w be $m_w$. Then $m_v\times m_w=-1$. So $9\times m_w = - 1$, and $m_w=-\frac{1}{9}$.

Step2: Use the point - slope form to find the equation of line w

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)=(3,-2)$ and $m =-\frac{1}{9}$. Substituting these values, we get $y-(-2)=-\frac{1}{9}(x - 3)$.

Step3: Convert to slope - intercept form

Simplify the point - slope equation: [ \begin{align*} y + 2&=-\frac{1}{9}x+\frac{1}{3}\ y&=-\frac{1}{9}x+\frac{1}{3}-2\ y&=-\frac{1}{9}x+\frac{1 - 6}{3}\ y&=-\frac{1}{9}x-\frac{5}{3} \end{align*} ]

Answer:

$y =-\frac{1}{9}x-\frac{5}{3}$