Question

a city planner wants to build a road perpendicular to d street. what should be the slope of the new road? slope =

Explanation:

Step1: Find slope of D - Street

D - Street is a vertical line. The equation of a vertical line is of the form $x = a$ (where $a$ is a constant). For a vertical line, the change in $x$ ($\Delta x$) between any two points is 0. The slope formula is $m=\frac{\Delta y}{\Delta x}$. Since $\Delta x = 0$ for a vertical line, the slope of D - Street is undefined.

Step2: Determine slope of perpendicular line

If two lines are perpendicular, and the slope of one line is $m_1$ and the slope of the other is $m_2$, then $m_1\times m_2=- 1$. A line perpendicular to a vertical line is a horizontal line. The equation of a horizontal line is of the form $y = b$ (where $b$ is a constant). For a horizontal line, the change in $y$ ($\Delta y$) between any two points is 0. Using the slope formula $m=\frac{\Delta y}{\Delta x}$, when $\Delta y = 0$, the slope $m = 0$.

Answer:

0