# 5.16. Free Response Question - 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://apstudents.collegeboard.org/courses/ap-computer-science-a/free-response-questions-by-year.

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
```

## 5.16.1. 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 (using the equation `-a / b`) and a method `isOnLine(x,y)` 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, by testing if `ax + by + c` is equal to 0.

Your class must produce the indicated results when the main method below is run. You may ignore any issues related to integer overflow.

Write a class APLine with instance variables, a constructor with 3 paramaters for a, b, c, and the methods getSlope() and isOnLine(x,y).

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