Equations of parallel lines

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

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Elliott Fletcher 7 years, 8 months ago

Published this.

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Christian Lawson-Perfect 7 years, 9 months ago

Gave some feedback: Ready to use

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Christian Lawson-Perfect 7 years, 9 months ago

Saved a checkpoint:

I've fixed a lot of typos, but otherwise this looks good!

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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

I'm not sure I want to include the same graph and part b, so I'm open to any suggestions of ways to introduce the 5 line equations.

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Bradley Bush 7 years, 9 months ago

Created this as a copy of Equations of straight lines MCQ.

Name	Status	Author	Last Modified
Equations of straight lines MCQ	Ready to use	Bradley Bush	20/11/2019 14:37
Equations of parallel lines	Ready to use	Bradley Bush	20/11/2019 14:37
Ida's copy of Equations of straight lines MCQ	draft	Ida Landgärds	12/04/2018 14:04
Identifiera graf med ekvation	draft	Ida Landgärds	12/04/2018 14:05
Spørsmål 2	draft	Ida Landgärds	13/03/2023 08:46
Dadas las ecuaciones de rectas paralelas....	Ready to use	Luis Hernandez	14/12/2020 18:36

There are 12 other versions that do you not have access to.

Question statement

Use the graph bellow to wok out the line equations of lines $A_0 \text{ to } E_0$ and use these equations to judge which lines they are parallel to.

{geogebra_applet('WuavQqEG',[["m1",m1],["m2",m2],["m3",m3],["c1",c1],["c2",c2],["c3",c3],["c4",c4],["c5",c5],["f1",f1],["d1",d1],["a1",a1],["b1",b1]])}

Give any introductory information the student needs.

			Name	Type	Generated Value

m1	number	1.5
m2	number	1.5
m3	number	-1.7
mfake	integer	-4
muniq	integer	10

			Name	Type	Generated Value

c1	integer	-8
c2	integer	18
c3	integer	3
c4	integer	5
c5	integer	17
cfake	integer	-5
cpar	integer	746

			Name	Type	Generated Value

a1	integer	30
b1	integer	25
c10	number	17.6470588235
d1	integer	60
f1	integer	-40

			Name	Type	Generated Value

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(1..2#0.1)

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: `number`

1.5

→ Used by:

m2
muniq

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Gap 0. Choose one from a list
  Add
2. Gap Gap 1. Choose one from a list
  Add
3. Gap Gap 2. Choose one from a list
  Add
4. Gap Gap 3. Choose one from a list
  Add
5. Gap Gap 4. Choose one from a list
  Add
6. Gap Gap 5. Choose one from a list
  Add
Part b) Match choices with answers
Part c) Choose several from a list
Part d) Choose several from a list
Part e) Choose several from a list
Part f) Choose several from a list
Part g) 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.

Fill in the gaps below to complete the description of parallel lines.

Parallel lines are defined as a lines that remain Gap 0. distance apart and so they never meet. This means that their Gap 1. is the same.

If we write our line equations in the form $y=m_i\times x_i+c_i$, then for parallel lines, Gap 2. $=$ Gap 3..

Vertical lines are always parallel to Gap 4. and horizontal lines are always parallel to Gap 5..

Advice

a)

Parallel lines are defined as lines that remain the same distance apart and so they never meet. This means that their gradient is the same.

If we write our line equations in the form $y_i=m_i\times x_i+c_i$, then for parallel lines, $m_1=m_2$.

Vertical lines are always parallel to the $y$-axis and horizontal lines are always parallel to the $x$-axis.

b)

All but one of the straight lines above follow the general formula $y=mx+c$ where $m$ is a constant denoting the gradient of the line and $c$ is a constant denoting the $y$-intercept of the line.

The gradient (given by $m$), indicates the slope of a straight line. Where this is positive, the $y$-coordinate along the line increases by $m$ for every increase in the value of $x$ by $1$. For example, $y=3x$ indicates that for every increase in the value of $x$ by $1$, the value of $y$ increases by $3$. Where there is no $m$ (i.e. $y=c$), the line is horizontal as the value of $y$ has no dependence on the value of $x$.

The $y$-intercept (given by $c$), indicates the point where the line passes through the $y$-axis. If the line equation has no $c$ (i.e. $y=mx$), the line has a $y$ intercept of $0$ (passing through the origin).

We can use our knowledge of the slope of the line and the $y$-intercept to then judge which points on the graph correspond to which equations.

$y=\simplify{{m1}x+{c1}}$ gives us $m=\var{m1}$ and $c=\var{c1}$.

$y=\simplify{{m2}x+{c2}}$ gives us $m=\var{m2}$ and $c=\var{c2}$.

$y=\simplify{{m3}x+{c3}}$ gives us $m=\var{m3}$ and $c=\var{c3}$.

$y=\simplify{{c4}}$ gives us $m=0$ and $c=\var{c1}$.

$x=\var{c5}$ is the exception to the $y=mx+c$ form of writing straight line equations. This equation gives a value for $x$ independent of the value of $y$, so a vertical line is formed at the $x$-coordinate $\var{c5}$.

c)

For the equation $y=\var{cfake}$, the gradient is $0$, so we check our lines $A_0, B_0, C_0, D_0 \text{ and }E_0$ to find $D_0$ has the same gradient. Therefore $D_0$ is parallel to $y=\var{cfake}$.

d)

For the equation $y=\var{m1}x+\var{cpar}$, the gradient is $\var{m1}$, so we check our lines $A_0, B_0, C_0, D_0 \text{ and }E_0$ to find both $A_0$ and $B_0$ have the same gradient. Therefore $A_0$ and $B_0$ are parallel to $y=\var{m1}x+\var{cpar}$.

e)

This time, we have to find the gradient of the $x$-axis. Note that the $x$-axis is equivalent to the line with equation $y=0$. The gradient of this line is $0$, so we check our lines $A_0, B_0, C_0, D_0 \text{ and }E_0$ to find $D_0$ has the same gradient. Therefore $D_0$ is parallel to $y=0$ and in other words, $D_0$ is parallel to the $x$-axis.

f)

For the equation $y=\simplify{{muniq}x+{c1}}$, the gradient is $\var{muniq}$, so we check our lines $A_0, B_0, C_0, D_0 \text{ and }E_0$ to find none have the same gradient. Therefore none of the labelled lines are parallel to $y=\simplify{{muniq}x+{c1}}$.

g)

Lines that are parallel have the same gradient. This is represented by $m$ in the general form of a straight line ($y=mx+c$). The gradient of $C_0$ was $\var{m3}$, so any straight line parallel to $C_0$ will share this value for $m$.

Therefore, we input $y=\var{m3}x+c$.

Give a worked solution to the whole question.

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This question is used in the following exams:

maths practice-revision by David Martin in David's workspace.
Week 2 Homework by Deirdre Casey in IFY DIFC.
Parallel and Perpendicular lines by haifa abd in NEM1001.
P2 - Coordinate Geometry by Rob Beckett in Rob's workspace.
MEM23004A by Mykola Kyrylenko in Mykola's workspace.
Module 3 by Niharika Singh in Niharika's workspace.
Week 4: Straight Lines by Amy Barker in Maths and Stats.
Transition Geometry by Chris Templet in Chris's workspace.
Week 2: Straight Lines by Amy Barker in Maths and Stats.
All the good stuff by Chris Templet in Chris's workspace.
Week 1 Diagnostic test by Anne-Sophie Kaloghiros in MA1630 - Fundamentals of Mathematics 2024-2025.

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Elliott Fletcher 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 9 months ago

Christian Lawson-Perfect 7 years, 9 months ago

Bradley Bush 7 years, 9 months ago

Bradley Bush commented 7 years, 9 months ago

Bradley Bush 7 years, 9 months ago

Error in variable testing condition

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Warning

Generated value: `number`

Parts

Gap-fill

a)

b)

c)

d)

e)

f)

g)

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Equations of parallel lines

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Elliott Fletcher 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 9 months ago

Christian Lawson-Perfect 7 years, 9 months ago

Bradley Bush 7 years, 9 months ago

Bradley Bush commented 7 years, 9 months ago

Bradley Bush 7 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Gap-fill

a)

b)

c)

d)

e)

f)

g)

Generated value: `number`