# 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).