Linear graphs: Read a gradient from a graph

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Ruth Hand

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Ruth Hand

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Ready to use

3 years, 7 months ago

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Christian Lawson-Perfect 2 years, 7 months ago

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Ruth Hand 3 years, 7 months ago

Gave some feedback: Ready to use

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Ruth Hand 3 years, 7 months ago

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Name	Status	Author	Last Modified
Linear graphs: Read a gradient from a graph	Ready to use	Ruth Hand	16/01/2023 14:16
Linear graphs: calculate gradient	Ready to use	Ruth Hand	27/09/2022 09:01
Linear graphs: Reading gradient and intercept from an equation	Ready to use	Ruth Hand	17/04/2024 11:14
Linear graphs: Find equation of a line 1	Ready to use	Ruth Hand	27/09/2022 09:01
CA1 Straight Line Graphs	Ready to use	Megan Oliver	17/04/2025 09:02

There are 15 other versions that do you not have access to.

Question statement

{app}
Find the gradient of the line.

Give any introductory information the student needs.

			Name	Type	Generated Value

app	ggbapplet	HTML node
m	rational	4
c	rational	0
P1	vector	vector(0,0)
P2	vector	vector(1,4)
uod	string	going up
ax	integer	0
ay	integer	0
bx	integer	1
by	integer	4
app_advice	ggbapplet	HTML node
p3	vector	vector(1,0)
pon	string	a positive number
sos	string	steep
mol	string	greater than or equal to 1

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
geogebra_applet(
  800,500,
  [
    A: [
      definition: p1,
      label_visible: false,
      visible: false
    ],
    B: [
      definition: p2,
      label_visible: false,
      visible: false      
    ],
    line: [
      definition: "Line(A,B)",
      label_visible: false
    ]
  ]
)

JME function reference

This variable is an interactive HTML node. Interactive HTML nodes can not be relied upon to work correctly when resuming a session - for example, attached event callbacks will be lost, and mathematical notation will likely also break.

If this causes problems, try to create HTML nodes where you use them in content areas, instead of storing them in variables.

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: `ggbapplet`

GeoGebra applet loading...

← Depends on:

This variable doesn't seem to be used anywhere.

Advice

Firstly draw a right angled 'step' from left to right. This triangle can be anywhere, but it is more helpful for it to have corners on the vertices (whole number points) of the graph and it is easier to calculate with postive numbers.

{app_advice}

Before we start to calculate, notice that the line is {uod}, so the gradient will be {pon} and the line is {sos}, so the absolute value of the number will be {mol}.

Now find the coordinates of the places your triangle meets the line

$(x_1,y_1)=(\var{ax},\var{ay})$ and $(x_2,y_2)=(\var{bx},\var{by})$

We need to compare the 'rise on the y-axis' to the 'run across the x-axis', we can say that:

$\text{gradient} = \frac{\text{rise}}{\text{run}}$

This is equivalent to using the formula:

$ m = \frac{y_2 - y_1}{x_2 - x_1} $

and substitute the coordinates of the vertices of the triangle:

$\begin{split} &\, m = \frac{\var{by} - \var{ay}}{\var{bx} - \var{ax}} \\
&\, = \frac{\var{by-ay}}{\var{bx-ax}} \\
&\, = \var[fractionNumbers]{m} \\
\end{split} $

Give a worked solution to the whole question.

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Part	Test	Passed?
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Mathematical expression		Hasn't run yet
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Mathematical expression		Hasn't run yet

This question is used in the following exams:

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Straight Lines pre-A level by Ruth Hand in MASH Bath: Moodle quizzes and TS.
Core Maths Test 2025 by Angus Rosenburgh in Angus's workspace.

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Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

Christian Lawson-Perfect 2 years, 7 months ago

Ruth Hand 3 years, 7 months ago

Ruth Hand 3 years, 7 months ago

Error in variable testing condition

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Generated value: `ggbapplet`

Parts

Mathematical expression

Advanced settings

Checking accuracy

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Linear graphs: Read a gradient from a graph

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Christian Lawson-Perfect 2 years, 7 months ago

Ruth Hand 3 years, 7 months ago

Ruth Hand 3 years, 7 months ago

Error in variable testing condition

Error

Warning

Generated value: ggbapplet

Parts

Mathematical expression

Advanced settings

Checking accuracy

Variable value generators

Pattern restriction

Variables

String restrictions

Generated value: `ggbapplet`