** Using WeBWorK **

For each graph, determine its system of linear inequalities. 1. A. B. C. D. E. F. None of the above 2. A. B. C. D. E. F. None of the above

##DESCRIPTION
##KEYWORDS('')
##
##ENDDESCRIPTION

DOCUMENT();        # This should be the first executable line in the problem.

loadMacros(
"PG.pl",
"PGbasicmacros.pl",
"PGchoicemacros.pl",
"PGanswermacros.pl",
"PGgraphmacros.pl"
);

TEXT(beginproblem());
$showPartialCorrectAnswers = 1;

$a = random(2,5,1);
$b = random(2,5,1);
while ($a == $b) {$b = random(2,5,1);}

$graph1 = init_graph(-3,-3,6,6, 'axes'=>[0,0],'grid'=>[9,9]);

$f3 = FEQ("x/($a) for x in <0,6> using color:black and weight:2");
$f4 = FEQ("$b * x for x in <0,6> using color:black and weight:2");

($f3Ref,$f4Ref) = plot_functions($graph1,$f3,$f4);

$mc1 = new_multiple_choice();

$graph1->fillRegion([1,1,'yellow']);

$mc1->qa(image(insertGraph($graph1),height=>200,width=>200), 
         "\( \left\{ \begin{array}{rcl}
         y & \le & $b x \cr
         x & \le & $a y 
         \end{array}\right. \)");

$mc1->extra("\( \left\{ \begin{array}{rcl}
            y & \ge & $b x \cr
            x & \le & $a y 
            \end{array}\right. \)",
"\( \left\{ \begin{array}{rcl}
y & \ge & $b x \cr
x & \ge & $a y 
\end{array}\right. \)",
         "\( \left\{ \begin{array}{rcl}
         y & \le & $b x \cr
         x & \ge & 0 
         \end{array}\right. \)",
"\( \left\{ \begin{array}{rcl}
y & \ge & $a x \cr
x & \ge & $b y 
\end{array}\right. \)");

$mc1->makeLast('None of the above');


$c = non_zero_random(-2,2,1); 

$graph2 = init_graph(-3,-3,6,6, 'axes'=>[0,0],'grid'=>[9,9]);

$k3 = FEQ("$c for x in <0,6> using color:black and weight:2");
$k4 = FEQ("x+$c for x in <0,6> using color:black and weight:2");

($k3Ref,$k4Ref) = plot_functions($graph2,$k3,$k4);

$fill_point_y = $c + 0.5;

$graph2->fillRegion([1,$fill_point_y,'yellow']);

$mc2 = new_multiple_choice();

$mc2->qa(image(insertGraph($graph2),height=>200,width=>200), 
         "\( \left\{ \begin{array}{rcl}
         y & \le & x + $c \cr
         y & \ge & $c 
         \end{array}\right. \)");

$mc2->extra("\( \left\{ \begin{array}{rcl}
         x & \le & y - $c \cr
         y & \ge & $c 
         \end{array}\right. \)",
"\( \left\{ \begin{array}{rcl}
y & \le & x \cr
y & \le & $c 
\end{array}\right. \)",
         "\( \left\{ \begin{array}{rcl}
         y & \le & x + $c \cr
         x & \ge & $c 
         \end{array}\right. \)",
"\( \left\{ \begin{array}{rcl}
y & \le & - x - $c \cr
y & \le & $c 
\end{array}\right. \)");

$mc2->makeLast('None of the above');

BEGIN_TEXT

For each graph, determine its system of linear inequalities. $BR

1.

\{ $mc2->print_q() \}
\{ $mc2->print_a() \}

END_TEXT

ANS(radio_cmp($mc2->correct_ans));

BEGIN_TEXT

2.

\{ $mc1->print_q() \}
\{ $mc1->print_a() \}

END_TEXT

ANS(radio_cmp($mc1->correct_ans));


ENDDOCUMENT();       # This should be the last executable line in the problem.

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