Graph Tool, plotting a line

Interactive graphing tool problem that asks the student to plot a line.

Complete Code

POD for Macro Files

parserGraphTool.pl

PG problem file

Explanation

DOCUMENT();

loadMacros('PGstandard.pl', 'PGML.pl', 'parserGraphTool.pl', 'PGcourse.pl');

Preamble

This example shows how to get student input in the form of a graph (a line) by using interactive graphing tools. Load the parserGraphTool.pl macro for this.

$x0   = non_zero_random(-6, 6);
$y0   = non_zero_random(-6, 6);
$line = nicestring([ $y0, $x0 ], [ 'x', 'y' ]);

$gt = GraphTool("{line, solid, ($x0, 0), (0, $y0)}")->with(
    bBox           => [ -11, 11, 11, -11 ],
    availableTools => [
        'PointTool',  'LineTool',
        'CircleTool', 'QuadraticTool',
        'CubicTool',  'FillTool',
        'SolidDashTool'
    ],
);

Setup

A cubic is created with 3 random zeros and a random y-intercept.

The GraphTool method creates the graph tool object. The only argument is the correct answer. This is a string that contains a list of objects that the student will be expected to graph. Each object is a brace delimited list of the attributes of the object. The first attribute in each list is the type of object to be graphed, line in this case. What the remaining attributes are depend on the type. For a line the second attribute is whether the object is to be solid or dashed, and the remaining attributes are two distinct points on the line.

The ->with method is then used to set options for the GraphTool object. In this case the options that are set are:

bBox: This is an array reference of four values xmin, ymax, xmax, ymin indicating the upper left and lower right corners of the visible graph.
availableTools: This determines which tools will be available for the student to use.

There is a default checker for the GraphTool that will mark correct a student answer that ‘looks’ like the correct one. For simple graphs, the default should be sufficient. See Graph Tool, custom checker for an example of how to use a custom checker.

BEGIN_PGML
On the graph below, plot the line [`[$line] = [$x0 * $y0]`].

[_]{$gt}
END_PGML

Statement.

The code [_]{$gt} inserts the GraphTool.

BEGIN_PGML_SOLUTION
Two points on the line are needed.  It could be put in slope-intercept form
which would give a [`y`]-intercept, and then a second point could be determined
from the slope.

Alternatively, the intercept form on the line is found by dividing both sides of
the equation by [`[$x0 * $y0]`] to get
[```\frac{x}{[$x0]} + \frac{y}{[$y0]} = 1.```]
Thus the [`x`]-intercept is the denominator of the fraction involving [`x`] or
[`[$x0]`] and the [`y`]-intercept is the denominator of the fraction involving
[`y`] or [`[$y0]`].

The solution is
[! the graph of the line through ([$x0],0) and (0,[$y0]) !]{$gt}
END_PGML_SOLUTION

ENDDOCUMENT();

Solution

A solution should be provided here.