Question

Heather is designing the drainage system for an apartment building. When a coordinate grid is placed on top of her design, two perpendicular pipes meet at the point (6,2), and one of the pipes is represented by the line y=1/2x +1 . What is the equation of the line representing the other pipe?

Answer 1

The equation of the line representing the other pipe in Heather's drainage system, which is perpendicular to the line y = 1/2x + 1 at the point (6,2), is y = -2x + 14.

Step-by-step explanation:

The equation for the line representing one of the pipes in Heather's drainage system design is given as y = 1/2x + 1, which has a slope of 1/2. Because the two pipes are perpendicular, the slope of the line representing the other pipe must be the negative reciprocal of 1/2, which is -2.

The pipes meet at the point (6,2), so we can use this point to determine the y-intercept of the second line.

To find the equation of the second line, we use the point-slope form which is y - y1 = m(x - x1) , where m is the slope and (x1, y1) is the point the line passes through. Substituting the known values, we get:

y - 2 = -2(x - 6)

Simplifying, we have:

y - 2 = -2x + 12
y = -2x + 14

Thus, the equation of the line representing the other pipe is y = -2x + 14.