the equation for line c can be written as y + 5 = -(x + 4). line d includes the point (-8, 2) and is…

Explanation:

Step1: Rewrite line c's equation in slope - intercept form

The equation of line c is $y + 5=-(x + 4)$, which can be rewritten as $y=-x - 4-5$ or $y=-x - 9$. The slope of line c, $m_1=-1$.

Step2: Find the slope of line d

If two lines are perpendicular, the product of their slopes is - 1. Let the slope of line d be $m_2$. Since $m_1\times m_2=-1$ and $m_1 = - 1$, then $(-1)\times m_2=-1$, so $m_2 = 1$.

Step3: Use the point - slope form to find the equation of line d

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)=(-8,2)$ and $m = 1$. Substituting these values, we get $y - 2=1\times(x+8)$.

Step4: Rewrite in slope - intercept form

Expand the point - slope equation: $y-2=x + 8$, then $y=x+8 + 2$, so $y=x + 10$.

Answer:

$y=x + 10$