## WeBWorK Main Forum

### point-slope form

by Carl Yao -
Number of replies: 0
Hello community:

I'm using ImplicitPlane context to ask students to input a line's equation in point-slope form. However, students can enter the equation in any form and the answer is still counted right. For example, if the answer I want is y-1=2(x-3), students can enter y=2x-5 and it's counted right.

If I use two text boxes _____=_____ and use Formula object in the second box, I cannot force students to enter 2(x-3). They can enter 2x-6 and it would still be counted right.

Has anyone written problems where students must enter point-slope form?

Codes are below. Thank you for any help!

Carl Yao
Portland Community College

# WeBWorK problem written by Carl Yao
# Portland Community College
#
# Given a line's slope and a point on the line, find the line's equation in
# both slope-intercept and point-slope form. All numbers are positive.
#
# Last edited: Yao 6/25/13
#
# ENDDESCRIPTION

## DBsubject('Algebra')
## DBchapter('Basic Algebra')
## DBsection('Slope-Intercept','Linear Equations','Point-Slope')
## KEYWORDS('slope','linear equation','slope-intercept','point-slope','line','equation')
## DBCCSS('8.F.3','A-CED')
## TitleText1('')
## EditionText1('')
## AuthorText1('')
## Section1('')
## Problem1('')
## Author('Carl Yao')
## Institution('PCC')

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

DOCUMENT();

"PGstandard.pl",
"MathObjects.pl",
"PGcourse.pl",
"PGML.pl",
"parserImplicitPlane.pl",
"parserAssignment.pl"
);

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

Context("Numeric");
parser::Assignment->Allow;

$m=random(2,5,1);$b=random(1,5,1);

$x1=random(1,5,1);$y1=$m*$x1+$b;$ansSI=Formula("y=$m*x+$b");

Context("ImplicitPlane");
Context()->variables->are(x=>'Real',y=>'Real');
Context()->flags->set(reduceConstants=>0);
$ansPS = ImplicitPlane("y=$m*x+$b"); ############################################## TEXT(beginproblem()); BEGIN_PGML A line's slope is [[$m]]. The line passes the point [([$x1],[$y1])]. Find this line's equation in both slope-intercept form and point-slope form.

Solution in slope-intercept form: [_______________]{$ansSI}. Solution in point-slope form: [________________]{$ansPS->cmp(correct_ans_latex_string=>"y-$y1 =$m(x-$x1)", correct_ans=>"y-$y1 = $m(x-$x1)"
),}.

END_PGML

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

$s1 =$m*$x1; BEGIN_PGML_SOLUTION *Find Equation in Slope-Intercept Form* To find a line's equation in slope-intercept form, we first write the formula [y=Mx+B], where [M] is the slope and [B] is the [y]-intercept. It's given that the slope is [[$m]], so we have [y=[$m]x+B]. Next, we need to plug in the point [([$x1],[y1])] and solve for [B]. [ \begin{alignedat}{2} y &= [m]x+B \\
[$y1] &= [$m] \cdot [$x1] +B \\ [$y1] &= [$s1] +B \\ -[$s1] & \quad -[$s1] \\ [$b] &= B
\end{alignedat}
]

The line's equation in slope-intercept form is [y=[$m]x+[$b]].

*Find Equation in Point-Slope Form*

To find a line's equation in point-slope form, we first write the formula [y-y_{1}=M(x-x_{1})], where [M] is the slope and [ (x_{1},y_{1}) ] is a point on the line.

Next, it's given the line's slope is [[$m]] and it passes the point [ ([$x1],[y1]) ]. We plug in these numbers into the formula, and we have: [ \begin{alignedat}{2} y-y_{1} &= M(x-x_{1}) \\ y-[y1] &= [$m](x-[$x1])
\end{alignedat}
]

The line's equation in point-slope form is [ y-[$y1] &= [$m](x-[\$x1]) ].

END_PGML_SOLUTION

ENDDOCUMENT();