Question

1. what is the slope of a line perpendicular to another line with a slope of 3? a -1/3 b 1/3 c -1 d 3 14. what is the slope of a vertical line? a 0 b undefined c any number d 1 15. which component of the distance formula represents the vertical difference between two points? a δx b δα c δy d δs

Explanation:

Step1: Recall perpendicular - slope rule

If the slope of a line is $m_1$ and the slope of a perpendicular line is $m_2$, then $m_1\times m_2=- 1$. Given $m_1 = 3$, we solve for $m_2$: $3\times m_2=-1$, so $m_2=-\frac{1}{3}$.

Step2: Recall slope of vertical line

The slope of a line is defined as $m=\frac{\Delta y}{\Delta x}$. For a vertical line, $\Delta x = 0$. Division by zero is undefined, so the slope of a vertical line is undefined.

Step3: Recall distance - formula components

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$, where $\Delta x=x_2 - x_1$ and $\Delta y=y_2 - y_1$. The vertical difference between two points is represented by $\Delta y$.

Answer:

1. A. $-\frac{1}{3}$
2. B. Undefined
3. C. $\Delta y$