the equation for line u can be written as y = -\\frac{9}{4}x + 1. line v, which is perpendicular to line u…

Explanation:

Step1: Find the slope of line v

The slope of line u is $m_{u}=-\frac{9}{4}$. For two perpendicular lines, the product of their slopes is - 1. Let the slope of line v be $m_{v}$. Then $m_{u}\times m_{v}=-1$. So $-\frac{9}{4}\times m_{v}=-1$, and $m_{v}=\frac{4}{9}$.

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

The point - slope form of a line is $y - y_{1}=m(x - x_{1})$, where $(x_{1},y_{1})=(-3,2)$ and $m = \frac{4}{9}$. Substitute these values into the formula: $y - 2=\frac{4}{9}(x+3)$.

Step3: Convert to slope - intercept form

Expand the right - hand side: $y - 2=\frac{4}{9}x+\frac{4}{3}$. Add 2 to both sides. Since $2=\frac{6}{3}$, then $y=\frac{4}{9}x+\frac{4 + 6}{3}$, so $y=\frac{4}{9}x+\frac{10}{3}$.

Answer:

$y=\frac{4}{9}x+\frac{10}{3}$