WW/pg 2.16

PGgraphmacros.pl

Here's one I've been working on.

##DESCRIPTION

## Point-slope form of a linear function

## Two points are randomly chosen to form the line. The points and

## the line are plotted.

##

##ENDDESCRIPTION

## DBsubject(Algebra)

## DBchapter(Linear equations and functions)

## DBsection(Equations of lines: point-slope form)

## Level(2)

## KEYWORDS('linear function', 'point-slope form')

DOCUMENT();

loadMacros(

"PGstandard.pl",

"MathObjects.pl",

"PGgraphmacros.pl",

"contextFraction.pl",

"PGML.pl",

"PGcourse.pl"

);

$refreshCachedImages=1;

TEXT(beginproblem());

Context("Fraction");

Context()->noreduce("(-x)-y");

Context()->noreduce('-n');

######################################

$xmin = -5;

$ymin = -5;

$xmax = 5;

$ymax = 5;

# Choose two points so that:

# neither is on the y-axis

# each at least 2 units apart in each direction

# the line through the points does not go through the origin

# the slope is not +1 or -1

do {

$x1 = non_zero_random(-4,4,1);

$b1 = random(-4,4,1);

do {$x2 = non_zero_random(-4,4,1);} until (abs($x2-$x1)>1);

do {$b2 = random(-4,4,1);} until ((abs($b2-$b1)>1) and ($b1*$x2-$b2*$x1 !=0));

$a1 = min($x1,$x2);

$a2 = max($x1,$x2);

$m = Fraction($b2-$b1,$a2-$a1);

} until (abs($m) != 1);

$f = Formula("$m*(x-$a1)+$b1")->reduce;

$f1 = Formula("$m*(x-$a2)+$b2")->reduce;

$f2 = Formula("$b2-$m*$a2 + $m*x")->reduce;

#----Build the graph

$graph = init_graph($xmin,$ymin,$xmax,$ymax,axes=>[0,0],size=>[400,400],grid=>[10,10]);

$graph->lb('reset');

add_functions( $graph,"$f for x in [$xmin,$xmax] using color:red and weight=2");

$graph->stamps( closed_circle($a1,$b1,'blue') );

$graph->stamps( closed_circle($a2,$b2,'blue') );

$i = 0; # Number the axes

do {

$xtick = $i + $xmin + 1;

$labelx[$i] = new Label($xtick,0, "$xtick",'black','center');

if ($xtick!=0) {$graph->lb($labelx[$i]);}

$i =$i+1;

} while ($i<($xmax-$xmin)-1);

$i = 0;

do {

$ytick = $i +$ymin + 1;

$labely[$i] = new Label(-.2,$ytick+.2, "$ytick",'black','center');

if ($ytick!=0) {$graph->lb($labely[$i]);}

$i =$i+1;

} while ($i<($ymax-$ymin)-1);

######################################

BEGIN_PGML

[@ image(insertGraph($graph),width=>400, height=>400, tex_size=>400) @]*

Use the graph given above to find the slope and equation for the line. Give the slope as an integer or fraction, no decimal values.

a) The slope of the line is [`m =`][______]{$m}

b) The equation of the line is [`y =`][__________________]{$f}

END_PGML

BEGIN_PGML_SOLUTION

Use the coordinates of the two blue dots to find the slope [`\ \displaystyle \frac{\Delta y}{\Delta x} = [$m]`]. The slope and one of the blue dots can be used to find the equation of the line using the point-slope form.

The solution, after simplifying, is [`y = [$f2]`]. Note: it is *not* necessary to simplify your equation.

END_PGML_SOLUTION

ENDDOCUMENT();