Equation de droite

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Alain Virouleau

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Needs to be tested

6 years, 9 months ago

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Alain Virouleau 6 years, 9 months ago

Gave some feedback: Needs to be tested

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Alain Virouleau 6 years, 9 months ago

Created this as a copy of Find the equation of a line through two points - positive gradient.

Name	Status	Author	Last Modified
Find the equation of a line through two points - positive gradient	Ready to use	Bradley Bush	03/02/2021 13:59
Find the equation of a line through two points - negative gradient	Ready to use	Bradley Bush	03/02/2021 13:59
Find the equation of a line through two points - zero gradient	Ready to use	Bradley Bush	03/02/2021 13:59
Straight line equation application: measuring sunflower height	Ready to use	Bradley Bush	03/02/2021 13:59
Louise's copy of Find the equation of a line through two points - positive gradient	draft	Louise Lynch	26/01/2022 19:48
Find the equation of a line through two points - positive gradient	draft	Mark Hodds	03/02/2021 13:59
Ida's copy of Find the equation of a line through two points - positive gradient	draft	Ida Landgärds	03/02/2021 13:59
Spørsmål 1	draft	Ida Landgärds	03/02/2021 13:59
Marte's copy of Find the equation of a line through two points - positive gradient	draft	Marte Bråtalien	03/02/2021 13:59
Thomas's copy of Find the equation of a line through two points - negative gradient	draft	Thomas Strasser	03/02/2021 13:59
Equation de droite	Needs to be tested	Alain Virouleau	30/05/2019 18:52
Linear Equations - Find the equation of a line through two points	draft	Paul Hancock	03/02/2021 13:59
Find the equation of a line through two points - positive gradient [L3]	Needs to be tested	Matthew James Sykes	03/02/2021 13:59
Beer Lambert Law	Doesn't work	Matthew James Sykes	03/02/2021 13:59
Beer Lambert Law Working Back up	Should not be used	Matthew James Sykes	03/02/2021 13:59
Joël's copy of Find the equation of a line through two points - positive gradient	draft	Jo Cohen	03/02/2021 13:59
Beer Lambert Law Working Back up	Should not be used	Matthew James Sykes	03/02/2021 13:59
Ida's copy of Spørsmål 1	draft	Ida Landgärds	09/01/2023 10:54
David's copy of Straight line equation application: measuring sunflower height	draft	David Rickard	03/02/2021 13:59
equation of a line through two points	draft	heike hoffmann	03/02/2021 13:59
Luis's copy of Find the equation of a line through two points - zero gradient	draft	Luis Hernandez	03/02/2021 13:59
Simon's copy of Equation of a line through two points - positive gradient	draft	Simon Thomas	03/02/2021 13:59
Maria's copy of Simon's copy of Equation of a line through two points - positive gradient	draft	Maria Aneiros	03/02/2021 13:59
Maria's copy of Find the equation of a line through two points - negative gradient	draft	Maria Aneiros	03/02/2021 13:59
Heather's copy of Find the equation of a line through two points - positive gradient	draft	Heather Driscoll	03/02/2021 13:59
Equation of a line through two points - positive gradient	draft	Heather Driscoll	03/02/2021 13:59
Equation of a line through two points	draft	Philip Charlton	03/02/2021 13:59
Find the equation of a line through two points - zero gradient	draft	Xiaodan Leng	03/02/2021 13:59
Equation of a line through two points - positive gradient	draft	Xiaodan Leng	03/02/2021 13:59
Straight line equation application: measuring sunflower height	draft	Adelle Colbourn	03/02/2021 13:59
Musa's copy of Find the equation of a line through two points	draft	Musa Mammadov	01/08/2022 08:15
Find the equation of a line through two points - positive gradient	Ready to use	Simon Vaughan	03/02/2021 13:59

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Question statement

Dans cette question, il s'agit de trouver une équation de droite de la forme $y=mx+c$ passant par deux points dont les coordonnées sont données.

Give any introductory information the student needs.

			Name	Type	Generated Value

x_a	integer	8
x_b	integer	-8
y_a	integer	-8
y_b	integer	7
m	rational	-15/16
c	rational	-1/2

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Generated value: `integer`

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Gap-fill
1. Gap Mathematical expression
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1. Step Step 0. Number entry
2. Step Step 1. Number entry

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Ask the student a question, and give any hints about how they should answer this part.

Donner l'équation de la droite passant par les points $A(\var{x_a}, \var{y_a})$ et $B(\var{x_b}, \var{y_b})$

$\displaystyle y=$ Unnamed gap

Advice

L'équation d'une droite passant par deux points se trouve en calculant le coefficient directeur de la droite et l'ordonnée à l'origine.

a)

On trouve le coefficient directeur ( $m$ ) en utiliant les points $A = (x_1,y_1)=(\var{x_a},\var{y_a})$ et $B = (x_2,y_2)=(\var{x_b},\var{y_b})$ grâce à la formule suivante :

$\begin{align} m &= \frac{y_2-y_1}{x_2-x_1} \\[0.5em] &= \frac{\simplify[!collectNumbers]{{y_b}-{y_a}}}{\simplify[!collectNumbers]{{x_b}-{x_a}}} \\[0.5em] &= \frac{\simplify[]{{y_b}-{y_a}}}{\simplify{{x_b}-{x_a}}} \\[0.5em] &= \simplify[simplifyFractions,unitDenominator]{({y_b-y_a})/({x_b-x_a})}\text{.} \end{align}$

b)

L'équation de la droite étant de la forme $y=mx+c$ , on trouve l'ordonnée à l'origine $c$ en utiisant les coordonnées d'un des deux points :

$c = y_1-mx_1 \quad \mathrm{ou} \quad c = y_2-mx_2 \,\text{.}$

Par exemple avec le point $A$ :

$\begin{align} c &= y_1-mx_1 \\ &= \var{y_a}-\var[fractionnumbers]{m}\times\var{x_a} \\ & = \simplify[fractionnumbers]{{y_a-m*x_a}}\text{.} \end{align}$

On injecte alors les valeurs calculées de $m$ et $c$ dans l'équation $y=mx+c$ et on obtient l'équation de droite:

$y=\simplify[!noLeadingMinus,fractionNumbers,unitFactor]{{m} x+ {c}}\text{.}$

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Alain Virouleau 6 years, 9 months ago

Alain Virouleau 6 years, 9 months ago

Error in variable testing condition

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Generated value: `integer`

Parts

Gap-fill

a)

b)

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Equation de droite

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Alain Virouleau 6 years, 9 months ago

Alain Virouleau 6 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

a)

b)

Generated value: `integer`