Question

1. a plumber is installing a new water pipe that needs to be perpendicular to a main drain line. the main drain line runs horizontally along the equation y = 12. the new water pipe must connect to a faucet located at (-7,3). what is the equation of the line representing the new water pipe? explain your reasoning.

Explanation:

Step1: Identify the slope of the main - drain line

The equation of the main - drain line is $y = 12$, which is a horizontal line. The slope of a horizontal line is $m_1=0$.

Step2: Determine the slope of the new water - pipe line

If two lines are perpendicular, the product of their slopes $m_1\times m_2=- 1$. Since $m_1 = 0$, the new line (perpendicular to the horizontal line) is a vertical line. The slope of a vertical line is undefined. The equation of a vertical line has the form $x = a$, where $a$ is a constant.

Step3: Find the equation of the new water - pipe line

The new water - pipe line passes through the point $(-7,3)$. For a vertical line passing through the point $(x_0,y_0)$, the equation is $x=x_0$. Here, $x_0=-7$. So the equation of the line representing the new water - pipe is $x=-7$.

Answer:

$x = - 7$