Find the equation of a line through two points - positive gradient

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From users who are members of Transition to university :

Chris Graham	said	Ready to use	7 years, 8 months ago
Christian Lawson-Perfect	said	Ready to use	7 years, 8 months ago
Bradley Bush	said	Needs to be tested	7 years, 9 months ago

From users who are not members of Transition to university :

Christopher boyd

said

Ready to use

7 years, 2 months ago

History

○

Chris Graham commented 6 years, 9 months ago

Fixed bug in correct line plot, caused by reading wrong student answer box (must have had a part added)

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Christopher boyd 7 years, 2 months ago

Gave some feedback: Ready to use

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Chris Graham 7 years, 8 months ago

Gave some feedback: Ready to use

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Christian Lawson-Perfect 7 years, 8 months ago

Gave some feedback: Ready to use

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Christian Lawson-Perfect 7 years, 8 months ago

Saved a checkpoint:

Made sure neither of the points lies on the $y$ -axis.

Split $a$ into two parts, since you need to work out the gradient before you find the $y$ intercept.

Reworded some of the advice a bit.

Restore this checkpoint

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Chris Graham 7 years, 8 months ago

Gave some feedback: Needs to be tested

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Chris Graham commented 7 years, 8 months ago

This was a bit of a mess, as the points A and B had originally been illogically ordered, and this had only been half fixed.

Part a) had mathematical expression gaps which should have been number entry, and I have added fractionNumbers simplification in the advice and displayed answer.

I've adjusted the axis ranges so that the intercept is always on the grid.

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Chris Graham commented 7 years, 8 months ago

The points A and B should be switched; it doesn't make sense to describe the leftmost point as B, and in fact the gradient is calculated from A to B in the advice. There are places in the advice where $y_1-y_2$ needs to be inverted.

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Chris Graham 7 years, 8 months ago

Gave some feedback: Has some problems

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Elliott Fletcher 7 years, 8 months ago

Published this.

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Chris Graham commented 7 years, 8 months ago

RE the point below from Aiden, this is OK, it is giving the student the opportunity to explore the terms in the equation and how they relate to the graph. This sort of question is really for formative use.

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Aiden McCall commented 7 years, 8 months ago

This is also true for all other questions of this nature.

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Aiden McCall 7 years, 8 months ago

Saved a checkpoint:

I have edited the main and advice to make sense and tweaked parts. There is a problem with the question that where you put y = mx +c you can write m in the gap fill and even when restricting the string it shows what m is on the graph so you can effectively 'cheat' this also works in the same way if you type in c. I cannot think of a way to fix this without the JSXgraph code and I don't know where abouts that is.

Restore this checkpoint

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Bradley Bush 7 years, 9 months ago

Gave some feedback: Needs to be tested

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Bradley Bush commented 7 years, 9 months ago

Thank you for the feedback Chris, I have done everything you've suggest4ed here as well as making the same changes to differenet versions of this question.

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Chris Graham commented 7 years, 9 months ago

One more. If I do not attempt the question, but reveal the answers, then the advice refers to an absent green line. This is another good reason to put the correct plot in the advice.

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Chris Graham commented 7 years, 9 months ago

Similar points to our earlier discussion:

This is a candidate for using the Numbas variables to set the jsxgraph axis limits. Move the block of code where you grab the Numbas variables in front of making the board, so that you have access to them. And then you can use them in the bounding box definition boundingBox:[yb-2,...] or whatever is sensible. Don't forget you'll want the intercept to be on the board.

Since you are only asking for the equation of the straight line through the points, you might consider creating a step with gapfills for the gradient and intercept, to allow the student to break the question down.

And you could add a second plot with the solution to the advice.

One final thing: on one run I had B at the origin. You may wish to avoid this as it makes parts of the advice obsolete.

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Chris Graham 7 years, 9 months ago

Gave some feedback: Has some problems

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Bradley Bush 7 years, 9 months ago

Gave some feedback: Needs to be tested

○

Bradley Bush 7 years, 9 months ago

Created this.

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

There are 102 other versions that do you not have access to.

Question statement

In this question we will identify the equation of the straight line passing through points $A=(\var{xa},\var{ya})$ and $B=(\var{xb},\var{yb})$ in the form $y = mx + c$.

{plotPoints()}

Give any introductory information the student needs.

			Name	Type	Generated Value

xa	integer	-4
xb	integer	-2
ya	integer	1
yb	integer	3
m	rational	1
c	rational	5

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(-4..-1)

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`

-4

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Number entry
  Add
Part b) Gap-fill
1. Gap Number entry
  Add
Part c) Gap-fill
1. Gap Mathematical expression
  Add

Gap-fill

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

Calculate the gradient, $m$, of the straight line between these two points.

$m=$ Unnamed gap

Advice

We find the equation of a straight line passing through two points by finding the gradient and the $y$-intercept of the line.

a)

We can find the gradient ($m$) using the points $A = (x_1,y_1)=(\var{xa},\var{ya})$ and $B = (x_2,y_2)=(\var{xb},\var{yb})$.

As the definition of gradient is the ratio of vertical change ($y_2-y_1$) to horizontal change ($x_2-x_1$).
The equation for gradient is,

\begin{align}
m &= \frac{y_2-y_1}{x_2-x_1} \\[0.5em]
&= \frac{\simplify[!collectNumbers]{{yb}-{ya}}}{\simplify[!collectNumbers]{{xb}-{xa}}} \\[0.5em]
&= \frac{\simplify[]{{yb}-{ya}}}{\simplify{{xb}-{xa}}} \\[0.5em]
&= \simplify[simplifyFractions,unitDenominator]{({yb-ya})/({xb-xa})}\text{.}
\end{align}

b)

Rearranging the equation $y=mx+c$ and substituting either of the points gives

\[c = y_1-mx_1 \quad \mathrm{or} \quad c = y_2-mx_2 \,\text{.} \]

We can then also use this equation with the other point's coordinates to check our answer.

Let's use point $A$ first:

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

We then check this against point $B$:

\[
\begin{align}
y_2 &= mx_2 + c \\[0.5em]
&= \simplify[fractionNumbers]{{m}{xb}+{c}} \\[0.5em]
&= \var[fractionnumbers]{m*xb+c}\text{.}
\end{align}
\]

c)

We can now substitute these values for $m$ and $c$ into $y=mx+c$ to get:

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

The green line drawn on the graph represents the above line equation.

{correctPoints()}

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

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

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Find the equation of a line through two points - positive gradient

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

Chris Graham commented 6 years, 9 months ago

Christopher boyd 7 years, 2 months ago

Chris Graham 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 8 months ago

Chris Graham 7 years, 8 months ago

Chris Graham commented 7 years, 8 months ago

Chris Graham commented 7 years, 8 months ago

Chris Graham 7 years, 8 months ago

Elliott Fletcher 7 years, 8 months ago

Chris Graham commented 7 years, 8 months ago

Aiden McCall commented 7 years, 8 months ago

Aiden McCall 7 years, 8 months ago

Bradley Bush 7 years, 9 months ago

Bradley Bush commented 7 years, 9 months ago

Chris Graham commented 7 years, 9 months ago

Chris Graham commented 7 years, 9 months ago

Chris Graham 7 years, 9 months ago

Bradley Bush 7 years, 9 months ago

Bradley Bush 7 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

a)

b)

c)

Generated value: `integer`