Question

write the equation of a line that is perpendicular to $y=-x - 6$ and that passes through the point $(-9,-4)$.

Explanation:

Step1: Find the slope of the perpendicular line

The slope of the given line $y=-x - 6$ is $m_1=-1$. For two perpendicular lines with slopes $m_1$ and $m_2$, $m_1\times m_2=- 1$. So, $-1\times m_2=-1$, then $m_2 = 1$.

Step2: Use the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)=(-9,-4)$ and $m = 1$. Substitute these values: $y-(-4)=1\times(x - (-9))$.

Step3: Simplify the equation

$y + 4=x + 9$, which can be rewritten as $y=x+5$.

Answer:

$y=x + 5$