Question

1. find the slope of the line that is parallel to y = -\frac{3}{4}x + 1.
2. find the equation of the line perpendicular to y = -\frac{2}{3}x - 4.
3. draw both a line that is parallel and a line that is perpendicular to the given line and goes through the given point.

Explanation:

Step1: Identify the slope of the given line

The equation of the given line is $y =-\frac{2}{3}x - 4$, which is in the slope - intercept form $y=mx + b$, where $m$ is the slope. So the slope of the given line $m_1=-\frac{2}{3}$.

Step2: Find the slope of the parallel line

Parallel lines have the same slope. So the slope of the line parallel to $y =-\frac{2}{3}x - 4$ is $m_{parallel}=-\frac{2}{3}$.

Step3: Find the slope of the 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 $m_1 =-\frac{2}{3}$, we get $-\frac{2}{3}\times m_{perpendicular}=-1$. Solving for $m_{perpendicular}$, we have $m_{perpendicular}=\frac{3}{2}$.

Answer:

The slope of the parallel line is $-\frac{2}{3}$ and the slope of the perpendicular line is $\frac{3}{2}$.