Question

consider the line y = -7 - 5x. 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: Identify the slope of the given line

The equation of the line is in the form $y = mx + b$, where $m$ is the slope. For the line $y=-7 - 5x$ or $y=-5x - 7$, the slope $m_1=-5$.

Step2: Find the slope of a parallel line

Parallel lines have equal slopes. So if the slope of the given line is $m_1=-5$, the slope of a parallel line $m_{parallel}=-5$.

Step3: Find the slope of a 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 $m_1 = - 5$ into the equation: $-5\times m_{perpendicular}=-1$. Solving for $m_{perpendicular}$, we get $m_{perpendicular}=\frac{1}{5}$.

Answer:

Slope of a perpendicular line: $\frac{1}{5}$
Slope of a parallel line: $-5$