Question

A walking path across a park is represented by the equation y=−3x−3. A new path will be built perpendicular to this path. The paths will intersect at the point (−3,6). Identify the equation that represents the new path.

A. y= 1/3x+7
B. y=3x+15
C. y=−3x−6
D. y=− 1/3x+5

Answer 1

The equation of the new path is y = 1/3x + 7.

Step-by-step explanation:

To find the equation of the new path, we need to determine the slope of the existing path. The given equation y = -3x - 3 represents the slope of -3. Since the new path will be perpendicular to the existing path, the slopes of the two paths are negative reciprocals of each other. So, the slope of the new path is 1/3.

Using the given point of intersection (-3, 6) and the slope 1/3, we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1). Plugging in the values, we get y - 6 = 1/3(x + 3). This equation can be simplified to y = 1/3x + 7, which represents the equation of the new path.

Therefore, the correct equation that represents the new path is y = 1/3x + 7 (Option A).