Solver Converting Linear Equations in Standard form to Slope-Intercept Form (and vice versa)

Source code of 'Converting Linear Equations in Standard form to Slope-Intercept Form (and vice versa)'

This Solver (Converting Linear Equations in Standard form to Slope-Intercept Form (and vice versa)) was created by by jim_thompson5910(35256)

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==section input
Please select the method of conversion *[choice form standard_to_slope-intercept slope-intercept_to_standard] form. For instance if you have a problem similar to {{{2x+3y=5}}} and you want to convert it to slope-intercept form, then choose "standard_to_slope-intercept".

If you have something similar to {{{y=2x+5}}} and you want to convert it to standard form then choose "slope-intercept_to_standard"

Input the equation in standard form {{{Ax+By=C}}} *[input A=1]x+ *[input B=2]y= *[input C=3]

Enter your equation in slope-intercept form ({{{y=mx+b}}} form)

y=*[input m=2]x + *[input y_intercept_b=1]

note: make sure you choose the correct form from the drop box above. Also, if you have decimal coefficients, convert them to fractions. For instance, if you have {{{.2x+.1y=10}}}, then input it as {{{(1/5)x+(1/10)y=10}}}

Edit: The solver has been updated (as of today's date July 29, 2017) which hopefully is more efficient and error-free. However, there may be other errors I didn't catch. Please let me know if you find any. As always, it's a good idea to check your answer.

==section solution

perl

################################## BEGIN Subroutines Section ##################################

sub my_gcf
{
  my ($x, $y) = @_;
  ($x, $y) = ($y, $x % $y) while $y;
  return $x;
}
#my $x = -5;
#my $y = -6;
#my $gcf = my_gcf($x,$y);
#print "Testing subroutine my_gcf$new_line_string";
#print "x = $x, y = $y, my_gcf(x,y) = $gcf$new_line_string";

sub my_lcm
{
  return($_[0] * $_[1] / my_gcf($_[0], $_[1]));
}

## Round any decimal number
sub my_round
{
   die "Needs 2 arguments" if @_ != 2;
   my ($number, $precision) = @_;
   my $answer;

$number =~ s/\s//g;

if( $number !~ m/\./ )
   {
      return $number;
   }

if( $precision == 0 )
   {
      return $number;
   }

my ($whole,$decimal) = split(/\./,$number);

#   if( length($decimal) == $precision )
#   {
#      $number = remove_trailing_zeros_after_decimal($number);
#      return $number;
#   }

if( length($decimal) <= $precision )
 {
 $number = remove_trailing_zeros_after_decimal($number);
 return $number;
 }

my ($captured_decimal,$next_digit) = $decimal =~ m/^(\d{$precision})(\d)/;

my $new_number = "$whole.$captured_decimal";

if( $next_digit >= 5 )
   {
      $new_number = $new_number + 1*10**(-1*$precision);
   }
   else
   {
   }
   $new_number = remove_trailing_zeros_after_decimal($new_number);
   return $new_number;
}
### Testing
#my $number = "6.955";
#my $precision = 2;
#my $ans = my_round($number,$precision);
#print "$number ---->  $ans ";

sub generate_fraction
{
   die "Only one argument allowed" if @_ != 1;
   my $x = $_[0];
   if($x!~ m/\//)
   {
      return ($x,1);
   }
   return split(/\//,$x);
}

## input: one fraction
## output: the reduced fraction (if it can be reduced), a flag indicating if reduction occurred
sub reduce_fraction
{
   die "Only one argument allowed" if @_ != 1;
   my $fraction = $_[0];
   my $ans = "";
   my $reduced_flag = 0;
   if($fraction !~ m/\//)
   {
      return ($fraction,$reduced_flag);
   }
   $fraction =~ s/$//g;
   $fraction =~ s/$//g;

my ($num,$denom) = split(/\//,$fraction);
   my ($num_sign,$denom_sign) = (0,0);
   if( $num =~ m/\-/ )
   {
      $num_sign = -1;
   }
   else
   {
      $num_sign = 1;
   }

if( $denom =~ m/\-/ )
   {
      $denom_sign = -1;
   }
   else
   {
      $denom_sign = 1;
   }

my $ans_sign = $num_sign/$denom_sign;

my $gcf = my_gcf(abs($num),abs($denom));

if(($gcf == 1) and ($denom_sign == 1))
   {
      #$reduced_flag = 0;
      return ($fraction,$reduced_flag);
   }
   else
   {
      $reduced_flag = 1;
   }

my $new_num = abs($num)/$gcf;
   my $new_denom = abs($denom)/$gcf;
   if( $new_denom == 1 )
   {
      $ans = $new_num;
   }
   else
   {
      $ans = "$new_num/$new_denom";
   }

if( $ans_sign == -1 )
   {
      $ans = "-$ans";
   }
   return ($ans,$reduced_flag);
}

################################## END Subroutines Section ####################################

################################## BEGIN Main Section ##################################

my $precision = 2;
my $new_line_string = ' ';

#print "($A,$B,$C,$m,$y_intercept_b) -->";
($A,$B,$C,$m,$y_intercept_b) = map{s/\s//g;$_} ($A,$B,$C,$m,$y_intercept_b);
#print " ($A,$B,$C,$m,$y_intercept_b)$new_line_string";
my $display_string = "";

## basic error checking (may not catch every case?)
my @input_array = ($A,$B,$C,$m,$y_intercept_b);
for (my $i=0;$i<scalar(@input_array);$i++)
{
 if($input_array[$i] =~ m/\./)
 {
 print "Error: No decimals allowed ( $input_array[$i] )$new_line_string";
 goto END_PROGRAM;
 }
 if($input_array[$i] =~ m/sqrt/)
 {
 print "Error: No square roots allowed ( $input_array[$i] )$new_line_string";
 goto END_PROGRAM;
 }
 if($input_array[$i] =~ m/log/)
 {
 print "Error: No logarithms allowed ( $input_array[$i] )$new_line_string";
 goto END_PROGRAM;
 } 
 if($input_array[$i] =~ m/(sin|cos|tan|csc|sec|cot|arcsin|arccos|arctan|arccsc|arcsec|arccot)/)
 {
 print "Error: No trig functions allowed ( $input_array[$i] )$new_line_string";
 goto END_PROGRAM;
 }
 if($input_array[$i] =~ m/[A-Z]|[a-z]/)
 {
 print "Error: Please only input numbers. Do not input letters of any kind ( $input_array[$i] )$new_line_string";
 goto END_PROGRAM;
 }
 if(($input_array[$i] =~ m/^\//) or ($input_array[$i] =~ m/\/$/))
 {
 print "Error: Division sign is in the wrong place for input $input_array[$i]$new_line_string";
 goto END_PROGRAM;
 } 
 
 
 my $temp1 = $input_array[$i];
 my @temp2 = $input_array[$i] =~ m/(\/)/g;
 
 if( scalar(@temp2) > 1 )
 {
 print "Error: There is more than one division sign in the input $input_array[$i]$new_line_string";
 goto END_PROGRAM; 
 }
 
 $temp1 =~ s/\///;
 $temp1 =~ s/\-//;
 if($temp1 =~ m/\D/)
 {
 print "Error: Not exactly sure what happened for the input $input_array[$i] but it's not a number$new_line_string";
 goto END_PROGRAM;
 }
}

if($form eq 'standard_to_slope-intercept')
{
   print "Convert from standard form (Ax+By = C) to slope-intercept form (y = mx+b)$new_line_string";

my $flag_A = 0;
   my $flag_B = 0;
   my $flag_C = 0;
   my ($num_A,$denom_A);
   my ($num_B,$denom_B);
   my ($num_C,$denom_C);
   my ($display_A,$display_B,$display_C);
   my ($temp1,$temp2,$temp3);
   my $LCD;
   if($A =~ m/\//)
   {
      ($num_A,$denom_A) = split(/\//,$A);
      $flag_A = 1;
      $display_A = "($A)";
   }
   else
   {
      ($num_A,$denom_A) = ($A,1);
      $display_A = $A;
   }

if($B =~ m/\//)
   {
      ($num_B,$denom_B) = split(/\//,$B);
      $flag_B = 1;
      $display_B = "($B)";
   }
   else
   {
      ($num_B,$denom_B) = ($B,1);
      $display_B = $B;
   }

if($C =~ m/\//)
   {
      ($num_C,$denom_C) = split(/\//,$C);
      $flag_C = 1;
      #$display_C = "($C)";
      $display_C = $C;
   }
   else
   {
      ($num_C,$denom_C) = ($C,1);
      $display_C = $C;
   }

$display_string = "$display_A"."x+$display_B"."y=$display_C";
   $display_string =~ s/\+\-/\-/g;
   print "{{{$display_string}}} Start with the given equation$new_line_string";
   my $original_equation=$display_string;

my ($new_A,$new_B,$new_C);
   if( ($flag_A == 1) or ($flag_B == 1) or ($flag_C == 1) )
   {
      $LCD = my_lcm($denom_A,$denom_B);
      $LCD = my_lcm($LCD,$denom_C);
      $display_string = "$LCD($display_A"."x+$display_B"."y)=$LCD($display_C)";
      $display_string =~ s/\+\-/\-/g;
      print "{{{$display_string}}} Multiply both sides by the LCD $LCD$new_line_string";
      #$new_A = my_round(eval($LCD*$A),$precision);
      #$new_B = my_round($LCD*$B,$precision);
      #$new_C = my_round($LCD*$C,$precision);
      $new_A = my_round(($LCD*$num_A)/($denom_A),2);
      $new_B = my_round(($LCD*$num_B)/($denom_B),2);
      $new_C = my_round(($LCD*$num_C)/($denom_C),2);
      $display_string = "$new_A"."x+$new_B"."y=$new_C";
      $display_string =~ s/\+\-/\-/g;
      print "{{{$display_string}}} Distribute and multiply (note how the fractions have been eliminated)$new_line_string";
   }
   else
   {
      ($new_A,$new_B,$new_C) = ($A,$B,$C);
   }

if($new_A =~ /\-/)
   {
      $temp1 = $new_A;
      $temp1 =~ s/\-//;
      $display_string = "$new_A"."x+$new_B"."y+$temp1"."x=$new_C+$temp1"."x";
      $display_string =~ s/\+\-/\-/g;
      print "{{{$display_string}}} Add $temp1",,"x to both sides$new_line_string";
   }
   else
   {
      $display_string = "$new_A"."x+$new_B"."y-$new_A"."x=$new_C-$new_A"."x";
      $display_string =~ s/\+\-/\-/g;
      print "{{{$display_string}}} Subtract $new_A",,"x from both sides$new_line_string";
   }

$display_string = "$new_B"."y=".((-1)*($new_A))."x+$new_C";
   $display_string =~ s/\+\-/\-/g;
   print "{{{$display_string}}} Simplify$new_line_string";
   
   my ($new_m,$reduced_flag1);
   my ($new_y_intercept_b,$reduced_flag2);

if( $new_B != 1 )
   {
      
      $display_string = "($new_B"."y)/($new_B)=(".((-1)*($new_A))."x+$new_C)/($new_B)";
      $display_string =~ s/\+\-/\-/g;
      print "{{{$display_string}}} Divide both sides by $new_B to isolate y$new_line_string";

$display_string = "y = (".((-1)*($new_A))."x)/($new_B)+($new_C)/($new_B)";
      $display_string =~ s/\+\-/\-/g;
      print "{{{$display_string}}} Break up the fraction on the right hand side$new_line_string";

($new_m,$reduced_flag1) = reduce_fraction("".((-1)*($new_A))."/$new_B");
      ($new_y_intercept_b,$reduced_flag2) = reduce_fraction("($new_C)/($new_B)");
      #if( ($reduced_flag1 == 1) or ($reduced_flag2 == 1))
      #{
         $display_string = "y = ($new_m)"."x+$new_y_intercept_b" if($new_m =~ m/\//);
         $display_string = "y = $new_m"."x+$new_y_intercept_b" if($new_m !~ m/\//);
         $display_string =~ s/\+\-/\-/g;
         print "{{{$display_string}}} Reduce and simplify$new_line_string";
      #}
	  
   }
   else
   {
      $display_string = "y = ".((-1)*($new_A))."x+$new_C";
      $display_string =~ s/\+\-/\-/g;
	  $new_m = (-1)*($new_A);
	  $new_y_intercept_b = $new_C;
   }

print "The original equation {{{$original_equation}}} (standard form) is equivalent to {{{$display_string}}} (slope-intercept form)$new_line_string";

print "The equation {{{$display_string}}} is in the form {{{y=mx+b}}} where {{{m=$new_m}}} is the slope and {{{b=$new_y_intercept_b}}} is the y intercept.$new_line_string";
   
}
## -------------------------------------------------------------------------- ##
if($form eq 'slope-intercept_to_standard')
{
   my $display_string = "";
   my ($new_m,$new_b);
   my ($temp1,$temp2,$temp3);
   print "Convert from slope-intercept form (y = mx+b) to standard form (Ax+By = C)$new_line_string";
   my ($num_m,$denom_m) = generate_fraction($m);
   my ($num_b,$denom_b) = generate_fraction($y_intercept_b);

my $LCD;
   #print "(num_m,denom_m) = ($num_m,$denom_m)$new_line_string";
   #print "(num_b,denom_b) = ($num_b,$denom_b)$new_line_string";

$display_string = "y = $m"."x+$y_intercept_b" if($denom_m == 1);
   $display_string = "y = ($m)"."x+$y_intercept_b" if($denom_m != 1);
   $display_string =~ s/\+\-/\-/g;
   print "{{{$display_string}}} Start with the given equation$new_line_string";
   my $original_equation = $display_string;

if(($denom_m != 1) or ($denom_b != 1))
   {
      $LCD = my_lcm($denom_m,$denom_b);
      $display_string = "$LCD*y = $LCD*($m"."x+$y_intercept_b)" if($denom_m == 1);
      $display_string = "$LCD*y = $LCD*(($m)"."x+$y_intercept_b)" if($denom_m != 1);
      $display_string =~ s/\+\-/\-/g;
      print "{{{$display_string}}} Multiply both sides by the LCD $LCD$new_line_string";

$new_m = my_round(($LCD*$num_m)/($denom_m),$precision);
      $new_b = my_round(($LCD*$num_b)/($denom_b),$precision);
      $display_string = "$LCD"."y = $new_m"."x+$new_b";
      $display_string =~ s/\+\-/\-/g;
      print "{{{$display_string}}} Distribute and multiply$new_line_string";
   }
   else
   {
      $LCD = 1;
      $new_m = $m;
      $new_b = $y_intercept_b;
   }
   ($A,$B,$C) = (-1*$new_m,$LCD,$new_b);

if( $new_m =~ m/\-/)
   {
      $temp1 = $new_m;
      $temp1 =~ s/\-//g;
      $display_string = "$LCD"."y+$temp1"."x = $new_m"."x+$new_b+$temp1"."x";
      $display_string =~ s/\+\-/\-/g;
      print "{{{$display_string}}} Add $temp1"."x to both sides$new_line_string";
   }
   else
   {
      $display_string = "$LCD"."y-$new_m"."x = $new_m"."x+$new_b-$new_m"."x";
      $display_string =~ s/\+\-/\-/g;
      print "{{{$display_string}}} Subtract $new_m"."x from both sides$new_line_string";
   }

$display_string = "$A"."x+$B"."y = $C";
   $display_string =~ s/\+\-/\-/g;
   print "{{{$display_string}}} Simplify$new_line_string";

if( $A =~ m/\-/ )
   {
      $display_string = "-1*($A"."x+$B"."y) = -1*($C)";
      $display_string =~ s/\+\-/\-/g;
      print "{{{$display_string}}} Multiply both sides by -1 to make the A coefficient positive (note: this step may be optional; it will depend on your teacher and/or textbook)$new_line_string";

($A,$B,$C) = (-1*$A,-1*$B,-1*$C);

$display_string = "$A"."x+$B"."y = $C";
      $display_string =~ s/\+\-/\-/g;
      print "{{{$display_string}}} Distribute and simplify$new_line_string";
   }
   print "The original equation {{{$original_equation}}} (slope-intercept form) is equivalent to {{{$display_string}}} (standard form where A > 0)$new_line_string";

print "The equation {{{$display_string}}} is in the form {{{Ax+By = C}}} where {{{A = $A}}}, {{{B = $B}}} and {{{C = $C}}}$new_line_string";

}

END_PROGRAM:

################################## END Main Section ####################################

==section output

==section check