Needing help with this C++ practice problem

The equation of a line in standard form is ax +by = c, where in both a and b cannot be zero, and a, b, and c are real numbers. If b is not equal to zero, then a/b is the slope of the line. If a=0, then it is a horizontal line, and if b=0, then it is a vertical line. The slope of a vertical line is undefined. Two lines are parallel if they have the same slope or both are vertical lines. Two lines are perpendicular if either one of the lines is horizontal and the other is vertical, or the product of their slopes is -1.

Design the class lineType to store a line. To store a line, you need to store the values of a (coefficient of x), b (coefficient of y), and c. The class must contain the following operations:

1. If a line is nonvertical, then determine its slope.
2. Determine if two lines are equal. (Two lines a₁x + b₁y = c₁ and a₂x + b₂y = c₂ are equal if either a₁=a₂, b₁=b₂, and c₁=c₂, or a₁=ka₂, b₁=kb₂, and c₁=kc₂, for some real number k.)
3. Determine if two lines are parallel.
4. Determine if two lines are perpendicular.
5. If two lines are not parallel, then find the point of intersection.

Add appropriate constructors to initialize variables of lineType.

Write a main driver program to test the class. Do not include any keyboard input with the program. Include enough examples so that it is obvious that all of the operations defined for the class are working correctly.

Break the program into three files:

1. implementation file (.cpp)
2. header file (.h)
3. main driver file (.cpp)