Final answer:
A city water department is proposing the construction of a new water pipe. The new pipe will be perpendicular to the existing pipe shown, passing through the point (1, 0).
The two pipes will intersect at the point (2/3, -4/3).
Step-by-step explanation:
To find the point of intersection between the two pipes, we need to determine the equation of the existing pipe and the equation of the proposed new pipe.
The existing pipe is given by the equation y = mx + b, where m is the slope and b is the y-intercept.
From the given information, we know that the existing pipe passes through the point (0, 2) and has a slope of -2/3. Therefore, the equation of the existing pipe is y = -2/3x + 2.
Since the new pipe is perpendicular to the existing pipe, its slope will be the negative reciprocal of the existing slope. The negative reciprocal of -2/3 is 3/2.
Using the point-slope form of a linear equation, we can write the equation of the new pipe as y - 0 = 3/2(x - 1). Simplifying this equation, we get y = 3/2x - 3/2.
To find the point of intersection, we need to solve the system of equations formed by the existing pipe equation and the new pipe equation.
Substituting the existing pipe equation into the new pipe equation, we get -2/3x + 2 = 3/2x - 3/2.
Solving for x, we find x = 2/3.
Substituting this value back into either equation, we find y = -4/3.
Therefore, the two pipes will intersect at the point (2/3, -4/3).