line u has an equation of y = -x + 7. line v is perpendicular to line u and passes through (-8, -1). what is…

Explanation:

Step1: Find the slope of line v

The slope of line $u$ is $m_{u}=- 1$. For two - perpendicular lines, the product of their slopes is $-1$. Let the slope of line $v$ be $m_{v}$. Then $m_{u}\times m_{v}=-1$. Substituting $m_{u}=-1$ into the equation, we get $(-1)\times m_{v}=-1$, so $m_{v}=1$.

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 $(x_{1},y_{1})=(-8,-1)$ and $m = m_{v}=1$. Substituting these values, we have $y-(-1)=1\times(x - (-8))$, which simplifies to $y + 1=x + 8$.

Step3: Rewrite the equation in slope - intercept form

Subtract 1 from both sides of the equation $y + 1=x + 8$. We get $y=x+7$.

Answer:

$y=x + 7$