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

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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(13794)

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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_input=2]x + *[input b_input=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}}}
==section solution

perl

sub clean{

@array=();

@hold=@array;

@array=split(//,$string);

$size=@array;

for($i=0;$i<3;$i++)
{
for($count=0;$count<$size;$count++)
{if(($array[$count]=~/\+/)&&($array[$count+1]=~/\-/))
 { delete $array[$count];
}}

for($count=0;$count<$size;$count++)
{if((($array[$count]=~/\+/)&&($array[$count+1]=~/\(/))&&($array[$count+2]=~/\-/))
 {delete $array[$count];
 delete $array[$count+1];
}}

for($count=0;$count<$size;$count++)
{if(($array[$count]=~/\-/)&&($array[$count+1]=~/\+/))
 { delete $array[$count+1];
}}

for($count=0;$count<$size;$count++)
{if(($array[$count]=~/\-/)&&($array[$count+1]=~/\-/))
 {delete $array[$count];
  $array[$count+1]="+";}}

for($count=0;$count<$size;$count++)
{if((($array[$count]=~/\-/)&&($array[$count+1]=~/\(/))&&($array[$count+2]=~/\-/))
 {delete $array[$count+2];
 $array[$count]="+";
}}

for($count=0;$count<$size;$count++)
{if((($array[$count]=~/\//)&&($array[$count+1]=~/1/))&&(($array[$count+2]=~/\)/)&&($array[$count+3]=~/\*/)))
 {delete $array[$count];
 delete $array[$count+1];
delete $array[$count+2];
   for($count1=$count+2;$count1>=0;$count1--)
     {if($array[$count1]=~/\(/)
        {delete $array[$count1];
          $count1=-1;}
     }
}}

for($count=0;$count<$size;$count++)
{if((($array[$count]=~/\//)&&($array[$count+1]=~/1/))&&($array[$count+2]=~/\+/))
 {delete $array[$count];
 delete $array[$count+1];
}}

for($count=0;$count<$size;$count++)
{if((($array[$count]=~/\//)&&($array[$count+1]=~/1/))&&($array[$count+2]!~/\d/))
 {delete $array[$count];
 delete $array[$count+1];
}}

}

#$string=@array;

$string=@hold;

}

sub invert{

$temp=$arr1[0];
$arr1[0]=$arr1[2];
$arr1[2]=$temp;

return ($arr1[0], "/", $arr1[2]);
}

sub mult{

$temp1=$arr1[0]*$arr2[0];
$temp2=$arr1[2]*$arr2[2];

#$temp1=$numer1*$numer2;
#$temp2=$denom1*$denom2;
return ($temp1,"/",$temp2);
}

sub add{

if(($arr1[2]==$arr2[2])&&(($arr1[2]!=0)&&($arr2[2]!=0)))
{$lcm=$arr1[2];}

if(($arr1[2]!=$arr2[2])&&(($arr1[2]!=0)&&($arr2[2]!=0)))
{
 for($count=1;$count<abs($arr1[2]*$arr2[2]);$count++)
  {if(($arr1[2]%$count==0)&&($arr2[2]%$count==0))
    {$gcf=$count;}
  }
$lcm=($arr1[2]*$arr2[2])/$gcf;
$temp=$lcm/$arr1[2];

$arr1[0]=($lcm/$arr1[2])*$arr1[0];
$arr2[0]=($lcm/$arr2[2])*$arr2[0];

$arr1[2]=($lcm/$arr1[2])*$arr1[2];
$arr2[2]=($lcm/$arr2[2])*$arr2[2];
}

$tempfrac1[0]=$arr1[0]+$arr2[0];
$tempfrac2[0]=$arr1[2];
return ($tempfrac1[0],"/",$tempfrac2[0]);
}

sub subtract{

$arr1[0]=($lcm/$arr1[2])*$arr1[0];
$arr2[0]=($lcm/$arr2[2])*$arr2[0];

$arr1[2]=($lcm/$arr1[2])*$arr1[2];
$arr2[2]=($lcm/$arr2[2])*$arr2[2];
}
$tempfrac1[0]=$arr1[0]-$arr2[0];
$tempfrac2[0]=$arr1[2];
return ($tempfrac1[0],"/",$tempfrac2[0]);
}

sub reduce{

if($arr1[2]!=0)
{
$store=$arr1[0]/$arr1[2];

if($store>0)
{
  $arr1[0]=abs($arr1[0]);
  $arr1[2]=abs($arr1[2]);
}

if(($store<0)&&($arr1[2]<0))
{
  $arr1[0]=0-$arr1[0];
  $arr1[2]=abs($arr1[2]);
}

if($arr1[0]%$arr1[2]==0)
{
  $quotient=$arr1[0]/$arr1[2];
  return ($quotient,"/",1);
}
}

for ($i=abs($arr1[0]*$arr1[2]); $i>1; $i--)
{
 if (($arr1[0]%$i==0)&&($arr1[2]%$i==0))
    {
       $arr1[0]/=$i;
       $arr1[2]/=$i;
       $j=$i;

}
}
return ($arr1[0],"/",$arr1[2]);
}

if($form eq 'standard_to_slope-intercept')
{

@a, @b, @c;

if($a=~/\//)
{@a=split(/\//,$a);

$a[2]=$a[1];
$a[1]="/";}

if($a!~/\//)
{$a[0]=$a;
$a[1]="/";
$a[2]=1;}

if($b=~/\//)
{@b=split(/\//,$b);

$b[2]=$b[1];
$b[1]="/";}

if($b!~/\//)
{$b[0]=$b;
$b[1]="/";
$b[2]=1;}

if($c=~/\//)
{@c=split(/\//,$c);

$c[2]=$c[1];
$c[1]="/";}

if($c!~/\//)
{$c[0]=$c;
$c[1]="/";
$c[2]=1;}

if($b[2]!=0)
{$b2=$b[0]/$b[2];}

if($a[2]!=0)
{$a2=$a[0]/$a[2];}

if($c[2]!=0)
{$c2=$c[0]/$c[2];}

$string="(@a)*x+(@b)*y=@c";

$string=clean();

@initial=@array;

print "

{{{@array}}}Start with the given equation

@abs=@a;

$abs[0]=abs($abs[0]);

$string="(@abs)*x";

$string=clean();

@abs=@array;

$string="(@b)*y=@c-(@a)*x";

$string=clean();

$size=@array;

print "

{{{@array}}} ", ($a[0]>0) ?  "Subtract {{{@abs}}} from both sides": "Add {{{@abs}}} to both sides";

@arr1=@b;
@temp_b=invert();

@arr1=@temp_b;
@temp_b=reduce();

$string="y=(@temp_b)(@c-(@a)*x)";

$string=clean();

print "

{{{@array}}} Multiply both sides by ";

$string="@temp_b";

$string=clean();

@distribute=@array;

print "{{{@distribute}}}";

$string="y=(@temp_b)(@c)-(@temp_b)(@a)x)";

$string=clean();

print "

{{{@array}}} Distribute {{{@distribute}}}";

@arr1=@temp_b;
@arr2=@c;
@temp_c=mult();

@arr1=@temp_b;
@arr2=@a;
@temp_a=mult();

$string="y=@temp_c-(@temp_a)x";

$string=clean();

print "

{{{@array}}} Multiply";

@arr1=("0","/",$temp_a[2]);
@arr2=@temp_a;
@temp_a=subtract();

$string="y=(@temp_a)*x+@temp_c";

$string=clean();

print "

{{{@array}}} Rearrange the terms";

@arr1=@temp_a;
@temp_a=reduce();

@arr1=@temp_c;
@temp_c=reduce();

$string="y=(@temp_a)*x+@temp_c";

$string=clean();

print "

{{{@array}}} Reduce any fractions";

@final=@array;

print "

So the equation is now in slope-intercept form ({{{y=mx+b}}}) where ";

$string="@temp_a";

$string=clean();

$slope1="@temp_a";

if($slope1=~/\//)
{@slope=split(/\//,$slope1);}

if($slope1!~/\//)
{$slope .="/1";
@slope=split(/\//,$slope1);}

@slope=($slope[0],"/",$slope[1]);

print "{{{m=@array}}} (the slope) and ";

$string="@temp_c";

$string=clean();

@arr1=@temp_c;
@y_int=reduce();

print "{{{b=@array}}} (the y-intercept)";
}

if($form eq 'slope-intercept_to_standard')
{
if($m_input=~/\//)
{@m_input=split(/\//,$m_input);

$m_input[2]=$m_input[1];
$m_input[1]="/";}

if($m_input!~/\//)
{$m_input[0]=$m_input;
$m_input[1]="/";
$m_input[2]=1;}

if($b_input=~/\//)
{@b_input=split(/\//,$b_input);

$b_input[2]=$b_input[1];
$b_input[1]="/";}

if($b_input!~/\//)
{$b_input[0]=$b_input;
$b_input[1]="/";
$b_input[2]=1;}

$string="y=(@m_input)*x+@b_input";

$string=clean();

@initial=@array;

print "

{{{@array}}}Start with the given equation

@abs=(abs($m_input[0]),"/",$m_input[2]);
$string="(@abs)*x";

$string=clean();

@abs1=@array;

$string="y-(@m_input)*x=@b_input";

$string=clean();

print "

{{{@array}}}", ($m_input[0]>0) ? "Subtract {{{@abs1}}} from both sides" : "Add {{{@abs1}}} to both sides";

$string="-(@m_input)*x+y=@b_input";

$string=clean();

print "

{{{@array}}} Rearrange";

if(($m_input[2]==1)&&($b_input[2]==1))
{
 
$string="-@m_input";

$string=clean();

@cleana=@array;

$string="1";

$string=clean();

@cleanb=@array;

$string="@b_input";

$string=clean();

@cleanc=@array;

print "

Now the equation is in standard form {{{Ax+By=C}}} where {{{A=@cleana}}}, {{{B=@cleanb}}}, and {{{C=@cleanc}}}";
}

if(($m_input[2]!=1)||($b_input[2]!=1))
{
 @arr1=@m_input;
 @arr2=@b_input;
 @temporary=add();

$string="$lcm(-(@m_input)*x+y)=$lcm(@b_input)";

$string=clean();
 print "

{{{@array}}} Multiply both sides by $lcm

$string="$lcm(-@m_input)x+$lcm*y=$lcm(@b_input)";

$string=clean();
 print "

{{{@array}}} Distribute

@arr1=($lcm,"/","1");
@arr2=@m_input;
@multiply1=mult();

@arr1=($lcm,"/","1");
@arr2=@b_input;
@multiply2=mult();

$string="-(@multiply1)*x+$lcm*y=@multiply2";

$string=clean();
 print "

{{{@array}}} Multiply";

@arr1=@multiply1;
@multiply1=reduce();
@arr1=@multiply2;
@multiply2=reduce();

$string="-(@multiply1)*x+$lcm*y=@multiply2";

$string=clean();

print "

{{{@array}}} Reduce";

$string="-@multiply1";

$string=clean();

@cleana=@array;

$string="$lcm";

$string=clean();

@cleanb=@array;

$string="@multiply2";

$string=clean();

@cleanc=@array;

print "

Now the equation is in standard form {{{Ax+By=C}}} where {{{A=@cleana}}}, {{{B=@cleanb}}}, and {{{C=@cleanc}}}

";
}

}

==section output

==section check
  angle=40 angle1=50