# 11.21.5. Free Response - APLine¶

The following is a free response question from 2010. It was question 2 on the exam. You can see all the free response questions from past exams at https://apstudent.collegeboard.org/apcourse/ap-computer-science-a/exam-practice.

Question 2. An APLine is a line defined by the equation `ax + by + c = 0`,where `a` is not equal to zero, `b` is not equal to zero, and `a`, `b`, and `c` are all integers. The slope of an APLine is defined to be the double value `-a / b` . A point (represented by integers `x` and `y`) is on an APLine if the equation of the APLine is satisfied when those `x` and `y` values are substituted into the equation. That is, a point represented by `x` and `y` is on the line if `ax + by + c` is equal to 0. Examples of two APLine equations are shown in the following table.

Assume that the following code segment appears in a class other than APLine. The code segment shows an example of using the APLine class to represent the two equations shown in the table.

```APLine line1 = new APLine(5, 4, -17);
double slope1 = line1.getSlope();        // slope1 is assigned -1.25
boolean onLine1 = line1.isOnLine(5, -2); // true because 5(5) + 4(-2) + (-17) = 0

APLine line2 = new APLine(-25, 40, 30);
double slope2 = line2.getSlope();        // slope2 is assigned 0.625
boolean onLine2 = line2.isOnLine(5, -2); // false because -25(5) + 40(-2) + 30 != 0
```

## 11.21.5.1. Try and Solve It¶

Write the APLine class. Your implementation must include a constructor that has three integer parameters that represent `a`, `b`, and `c`, in that order. You may assume that the values of the parameters representing `a` and `b` are not zero. It must also include a method `getSlope` that calculates and returns the slope of the line, and a method `isOnLine` that returns `true` if the point represented by its two parameters (`x` and `y`, in that order) is on the `APLine` and returns `false` otherwise. Your class must produce the indicated results when invoked by the code segment given above. You may ignore any issues related to integer overflow.