a given line has the equation 2x + 12y = - 1. what is the equation, in slope - intercept form, of the line…

Explanation:

Step1: Rewrite given line in slope - intercept form

First, rewrite $2x + 12y=-1$ as $y=mx + b$. Solve for $y$: $12y=-2x - 1$, so $y=-\frac{2}{12}x-\frac{1}{12}=-\frac{1}{6}x-\frac{1}{12}$. The slope of the given line $m_1 =-\frac{1}{6}$.

Step2: Find the slope of the perpendicular line

If two lines are perpendicular, the product of their slopes $m_1\times m_2=-1$. Let the slope of the perpendicular line be $m_2$. Since $m_1 =-\frac{1}{6}$, then $-\frac{1}{6}m_2=-1$, and $m_2 = 6$.

Step3: Use the point - slope form to find the equation

The point - slope form is $y - y_1=m(x - x_1)$. The line passes through the point $(0,9)$ where $x_1 = 0$ and $y_1 = 9$, and $m = 6$. $y-9=6(x - 0)$, which simplifies to $y=6x + 9$.

Answer:

$y = 6x+9$