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

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Simon Vaughan

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4 years, 8 months ago

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Simon Vaughan 4 years, 8 months ago

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Simon Vaughan 4 years, 8 months ago

Gave some feedback: Ready to use

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Simon Vaughan 4 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

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

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.

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Generated value: `integer`

-1

→ Used by:

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.

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Part	Test	Passed?
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Gap-fill
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Number entry
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Gap-fill
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Mathematical expression
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This question is used in the following exams:

Paul's copy of Practice for year 1 by Paul Verheyen in Paul's workspace.
Practice for year 1 by Simon Vaughan in PA1710.
Melissa's copy of Practice for year 1 by Melissa Heath in Melissa's workspace.
test by John Little in John's workspace.
Novry's copy of Practice for year 1 by Novry Erwina in Novry's workspace.
An equation of a straight line by Jinhua Mathias in Maths 2.

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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

Simon Vaughan 4 years, 8 months ago

Simon Vaughan 4 years, 8 months ago

Simon Vaughan 4 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

a)

b)

c)

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Error

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

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Simon Vaughan 4 years, 8 months ago

Simon Vaughan 4 years, 8 months ago

Simon Vaughan 4 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

a)

b)

c)

Generated value: `integer`