Gareth's copy of pasar variables Graphs I: Linear - Line equation

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Gareth Woods

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Gareth Woods 8 years, 6 months ago

Created this as a copy of pasar variables Graphs I: Linear - Line equation.

Name	Status	Author	Last Modified
Use student input in a JSXGraph diagram	Ready to use	Christian Lawson-Perfect	03/02/2021 13:53
Amplitude Modulation	Ready to use	Martin Johnston	24/01/2025 14:58
Graeme's copy of Amplitude Modulation	Ready to use	Graeme Chester	02/06/2016 15:23
Kirchoff's Law	Ready to use	Martin Johnston	24/01/2025 14:58
Martin's copy of Kirchoff's Law	Ready to use	Martin Johnston	24/01/2025 14:58
joshua's copy of Jinhua's copy of Equation of a line 2	Ready to use	joshua boddy	03/02/2021 13:59
Julie's copy of joshua's copy of Jinhua's copy of Equation of a line 2	Ready to use	Julie Crowley	03/02/2021 13:59
JSXGraph test	draft	Tore Gaupseth	03/02/2021 13:59
Using student input in a JSXGraph diagram	draft	Anthony Brown	03/02/2021 13:59
Graphs I: Linear - Line equation	Ready to use	Sarah Turner	03/02/2021 13:59
capturando respuestas del board de JSXGraph diagram	draft	Marlon Arcila	03/02/2021 13:59
pasar variables Graphs I: Linear - Line equation	draft	Marlon Arcila	03/02/2021 13:59
1: Linear Graph - Time vs. Orogen Elevation	Doesn't work	Luke Park	19/12/2022 17:23
Graphs I: Linear - Line equation	Ready to use	Nasir Firoz Khan	03/02/2021 13:59
Gareth's copy of pasar variables Graphs I: Linear - Line equation	draft	Gareth Woods	03/02/2021 13:59
Using student input in a JSXGraph diagram	draft	Marlon Arcila	14/11/2016 13:27
Hannah's copy of Graphs I: Linear - Line equation	draft	Hannah Bartholomew	03/02/2021 13:59
Find equation of line (negative and fractions points)	draft	Julie Crowley	03/02/2021 13:59
Find equation of line	draft	Ben Morris	03/02/2021 13:59
Lovkush's copy of Using student input in a JSXGraph diagram	draft	Lovkush Agarwal	03/02/2021 13:59
Harry's copy of Using student input in a JSXGraph diagram	draft	Harry Flynn	24/03/2017 10:39
MA1002 Find equation of line (negative and fractions points)	draft	Kieran Mulchrone	03/02/2021 13:59
Alex's copy of Using student input in a JSXGraph diagram	draft	Alex Van den Hof	03/02/2021 13:59
Joseph's copy of Using student input in a JSXGraph diagram	draft	Joseph Mastromatteo	03/02/2021 13:59
Edward's copy of Use student input in a JSXGraph diagram	draft	Edward Hall	27/09/2017 23:03
Edward's copy of Use student input in a JSXGraph diagram	draft	Edward Hall	27/09/2017 23:15
GraphTemplate	draft	Raymond Corrigan	03/02/2021 13:59
Graph1	draft	Raymond Corrigan	31/03/2018 11:10
Ashley's copy of GraphTemplate	draft	Ashley Cusack	03/02/2021 13:59
Paul's copy of Use student input in a JSXGraph diagram	draft	Paul Hancock	03/02/2021 13:59
Michael's copy of Use student input in a JSXGraph diagram	draft	Michael Hoffmann	03/02/2021 13:59
Michael's copy of Use student input in a JSXGraph diagram	draft	Michael Hoffmann	03/02/2021 13:59
Line through two points	draft	Maths Tutor	03/02/2021 13:59
Graph - Line equation	draft	heike hoffmann	03/02/2021 13:59
Ruth's copy of Use student input in a JSXGraph diagram	draft	Ruth Allison	03/02/2021 13:59
JSXGraph diagram	draft	Lars Hansson	03/02/2021 13:59
JSXGraph diagram	draft	Lars Hansson	03/02/2021 13:59
Terry's copy of Use student input in a JSXGraph diagram	draft	Terry Young	03/02/2021 13:59
Visualisation of limit definition of derivative	draft	Paul King	18/06/2020 15:49
Danny's copy of Use student input in a JSXGraph diagram	Has some problems	Danny Tan	03/02/2021 13:59
JSXGraph diagram	draft	Lars Hansson	03/02/2021 13:59
Thomas's copy of Use student input in a JSXGraph diagram	draft	Thomas Cottrell	03/02/2021 13:59
Graph question for Melissa	Needs to be tested	David Martin	16/08/2019 11:42
David's copy of Graph question for Melissa	draft	David Martin	16/08/2019 11:43

There are 142 other versions that do you not have access to.

Question statement

{eqnline()}

The above graph shows a line which has an equation of the form $y=ax+b$ where $a$ and $b$ are integers.

You are given two points on the line as indicated on the diagram.

$(0,\var{b}),\;\;(-1,\var{b-a})$.

Your task is to input the equation of the line.

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	-2
b	integer	1
c	integer	0

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(-3..3 except 0)

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `integer`

-2

→ Used by:

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Number entry
  Add
1. Step Information only
Part b) Gap-fill
1. Gap Mathematical expression
  Add
1. Step Information only

Gap-fill

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

Input the gradient of the line

Gradient $=$Unnamed gap

Advice

First Method.

We are given that the line goes through $(0,\var{b})$ and $(-1,\var{b-a})$ and the equation of the line is of the form $y=ax+b$

Hence:

1) At $x=0$ we have $y=\var{b}$, and this gives $\var{b}=a \times 0 +b =b$ on putting $x=0$ into $y=ax+b$.
So $b=\var{b}$.
2) At $x=-1$ we have $y=\var{b-a}$, and this gives $\var{b-a}=a \times (-1) +b =\simplify[all,!collectNumbers]{-a+{b}}$ on putting $x=-1$ into $y=ax+b$.
After rearranging we obtain $a=\simplify[all,!collectNumbers]{{b}-{b-a}}=\var{a}$.
So $a=\var{a}$.
So the equation of the line is $\simplify{y={a}*x+{b}}$.

Second Method.

The equation $y=ax+b$ tells us that the graph crosses the $y$-axis (when $x=0$) at $y=b$.
So looking at the graph we immediately see that $b=\var{b}$.
$a$ is the gradient of the line and is given by the change from $(-1,\var{b-a})$ to $(0,\var{b})$:
\[a=\frac{\text{Change in y}}{\text{Change in x}}=\frac{\simplify[all,!collectNumbers]{({b-a}-{b})}}{-1-0}=\var{a}\]

For more help on line graphs click on this link.

Give a worked solution to the whole question.

URL

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Part	Test	Passed?
Gap-fill
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Number entry
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Information only
Gap-fill
Gap-fill		Hasn't run yet
Mathematical expression
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Information only

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Gareth's copy of pasar variables Graphs I: Linear - Line equation

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Gareth Woods 8 years, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

Loading...

Error

Gareth's copy of pasar variables Graphs I: Linear - Line equation

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Gareth Woods 8 years, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`