the equation of line s is y = -\\frac{1}{9}x - 4. line t includes the point (1, 7) and is perpendicular to…

Explanation:

Step1: Find the slope of line t

The slope of line s is $m_s =-\frac{1}{9}$. For two perpendicular lines, the product of their slopes is - 1. Let the slope of line t be $m_t$. Then $m_s\times m_t=-1$. So $-\frac{1}{9}\times m_t = - 1$, and $m_t = 9$.

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

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)=(1,7)$ and $m = 9$. Substituting these values, we get $y - 7=9(x - 1)$.

Step3: Convert to slope - intercept form

Expand the right - hand side: $y-7 = 9x-9$. Then add 7 to both sides of the equation: $y=9x-9 + 7$, which simplifies to $y = 9x-2$.

Answer:

$y = 9x-2$