Question

consider the line x - 9y = -9. what is the slope of a line perpendicular to this line? what is the slope of a line parallel to this line? slope of a perpendicular line: slope of a parallel line:

Explanation:

Step1: Rewrite in slope - intercept form

The slope - intercept form is $y = mx + b$, where $m$ is the slope. Given $x-9y=-9$, we solve for $y$:
$-9y=-x - 9$, then $y=\frac{1}{9}x + 1$. So the slope of the given line $m_1=\frac{1}{9}$.

Step2: Find slope of parallel line

Parallel lines have the same slope. So the slope of a line parallel to the given line $m_{parallel}=m_1=\frac{1}{9}$.

Step3: Find slope of perpendicular line

The product of the slopes of two perpendicular lines is $- 1$. Let the slope of the perpendicular line be $m_{perpendicular}$. Then $m_1\times m_{perpendicular}=-1$. Substituting $m_1 = \frac{1}{9}$, we get $\frac{1}{9}\times m_{perpendicular}=-1$, so $m_{perpendicular}=-9$.

Answer:

Slope of a perpendicular line: $-9$
Slope of a parallel line: $\frac{1}{9}$