Solver DESCRIBE a linear EQUATION: slope, intercepts, etc

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==section input
Describe a line given by *[input a=2]x + *[input b=4]y = *[input c=6].

==section solution
perl
if( !$b ) {
  if( $a == 0 ) {
    print "Coefficients for both x and y are zero, this is a bad, meaningless equation.\n";
    return;
  }
  $x_intercept = $c/$a;
  $y_intercept = undef;
  print "this equation defines a vertical line. 
<UL>
  <LI> X intercept: $x_intercept. X intercept is the intersection of the line with the x axis. </LI>
  <LI> Y intercept: not defined (the line IS vertical)</LI>
  <LI> Slope: not defined, can be thought of as infinite</LI>
</UL>";
  print "{{{graph( 500, 500, $x_intercept-5, $x_intercept+5, -10, 10, 1000000x-1000000*$x_intercept ) }}}\n";
} else {
  if( $a ) {
    print "Equation {{{$a x + $b y = $c}}} describes a sloping line. For any 
equation ax+by+c = 0, slope is {{{-a/b = -$a/$b}}}.";
    $x_intercept = $c/$a;
    $y_intercept = $c/$b;
    $slope = -$a/$b;
    print "<UL><LI>X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x =  c/a. $c/$a = $x_intercept.</LI>";
    print "<LI>Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is $c/$b = $y_intercept.</LI>";
    print "<LI>Slope is -$a/$b = $slope.</LI>";
    print "<LI> Equation in slope-intercept form: y=$slope*x+$y_intercept.</LI></UL>";
    print "{{{graph( 500, 500, $x_intercept-8, $x_intercept+8, $y_intercept-8, $y_intercept+8, $slope*x+$y_intercept ) }}}\n";
  } else {
    $x_intercept = undef;
    $y_intercept = $c/$b;
    print "This equation defines a horizontal line. There is no X intercept. Y intercept is {{{$c/$b=$y_intercept}}}\n\n\n";
    print "{{{graph( 500, 500, -10, 10, $y_intercept - 10, $y_intercept+10, $c/$b ) }}}";
  }
}
 
==section output
slope 
x_intercept 
y_intercept

==section check

==section practice
perl
  $a = randint( -2, 6 );
  $b = randint( -3, 3 );
  $c = randint( -3, 3 );