# Check if given two straight lines are identical or not

Given two straight lines with co-efficients of there equations a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 respectively, the task is to check if the straight lines are identical or not.

Examples:

Input: a1 = -2, b1 = 4, c1 = 3, a2 = -6, b2 = 12, c2 = 9
Output: The given straight lines are identical

Input: a1 = 12, b1 = 3, c1 = 8, a2 = 7, b2 = -12, c2 = 0
Output: The given straight lines are not identical

Approach:

1. Given equations,
a1x + b1y + c1 = 0
a2x + b2y + c2 = 0
2. converting them to slope intercept form, we get
y = (-a1/b1)x +(-c1/b1)
y = (-a2/b2)x +(-c2/b2)
3. now, if the lines are identical then there slope and intercepts must be equal,
so,
-a1/b1 = -a2/b2
or, a1/a2 = b1/b2

also,
-c1/b1 = -c2/b2
so, c1/c2 = b1/b2
4. So, if two given straight lines are identical then there co-efficients should be proportional.

Below is the implementation of the above approach

## C++

 // C++ program to check if  // given two straight lines  // are identical or not     #include  using namespace std;     // Function to check if they are identical  void idstrt(double a1, double b1,              double c1, double a2,              double b2, double c2)  {      if ((a1 / a2 == b1 / b2)          && (a1 / a2 == c1 / c2)          && (b1 / b2 == c1 / c2))          cout << "The given straight"              << " lines are identical"              << endl;         else         cout << "The given straight"              << " lines are not identical"              << endl;  }     // Driver Code  int main()  {      double a1 = -2, b1 = 4,             c1 = 3, a2 = -6,             b2 = 12, c2 = 9;      idstrt(a1, b1, c1, a2, b2, c2);      return 0;  }

## Java

 // Java program to check if  // given two straight lines  // are identical or not  class GFG  {     // Function to check if they are identical  static void idstrt(double a1, double b1,                      double c1, double a2,                      double b2, double c2)  {      if ((a1 / a2 == b1 / b2)          && (a1 / a2 == c1 / c2)          && (b1 / b2 == c1 / c2))          System.out.println( "The given straight"         +" lines are identical");         else         System.out.println("The given straight"             + " lines are not identical");  }     // Driver Code  public static void main(String[] args)   {      double a1 = -2, b1 = 4,              c1 = 3, a2 = -6,              b2 = 12, c2 = 9;      idstrt(a1, b1, c1, a2, b2, c2);  }  }     // This code has been contributed by 29AjayKumar

## Python3

 # Python3 program to check if  # given two straight lines  # are identical or not     # Function to check if they are identical  def idstrt(a1, b1, c1, a2, b2, c2):      if ((a1 // a2 == b1 // b2) and         (a1 // a2 == c1 // c2) and          (b1 // b2 == c1 // c2)):          print("The given straight lines",                            "are identical");      else:          print("The given straight lines",                        "are not identical");     # Driver Code  a1, b1 = -2, 4 c1, a2 = 3,-6 b2, c2 = 12,9 idstrt(a1, b1, c1, a2, b2, c2)     # This code is contributed   # by mohit kumar

## C#

 // C# program to check if   // given two straight lines   // are identical or not  using System;     class GFG   {      // Function to check if they are identical   static void idstrt(double a1, double b1,                       double c1, double a2,                       double b2, double c2)   {       if ((a1 / a2 == b1 / b2)           && (a1 / a2 == c1 / c2)           && (b1 / b2 == c1 / c2))           Console.WriteLine( "The given straight"         +" lines are identical");          else         Console.WriteLine("The given straight"             + " lines are not identical");   }      // Driver Code   public static void Main(String[] args)   {       double a1 = -2, b1 = 4,               c1 = 3, a2 = -6,               b2 = 12, c2 = 9;       idstrt(a1, b1, c1, a2, b2, c2);   }   }      // This code contributed by Rajput-Ji

## PHP

 

Output:

The given straight lines are identical


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