Linear graphs: Find the equation of a line 2

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Ruth Hand

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2 years, 9 months ago

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Christian Lawson-Perfect 2 years, 7 months ago

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Ruth Hand 2 years, 9 months ago

Gave some feedback: Ready to use

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Ruth Hand 3 years, 7 months ago

Created this.

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Question statement

Give any introductory information the student needs.

			Name	Type	Generated Value

ax	integer	2
bx	integer	7
ay	integer	-9
by	integer	-6
m	rational	3/5
c	rational	-51/5

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(-10..10 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`

This variable doesn't seem to be used anywhere.

Advice

You can calculate the gradient first, and then substitute this into the equation $y=mx+c$ , and rearrange to find $c$ .

It is more efficient, however, to calculate the whole thing in one go, using the equation:

$\frac{y - y_1}{x - x_1} = \frac{y_2 - y_1}{x_2 - x_1}$

and then rearrange this into any suitable form.

In this question we have:
$(x_1, y_1) = (\var{ax}, \var{ay})$ and $(x_2, y_2) = (\var{bx}, \var{by})$

Therefore

$\begin{split} \frac{y - y_1}{x - x_1} &= \frac{y_2 - y_1}{x_2 - x_1} \\ \\ \frac{y - \var{ay}}{x - \var{ax}} &= \frac{\var{by} - \var{ay}}{\var{bx} - \var{ax}} \\ \\ \frac{y - \var{ay}}{x - \var{ax}} &= \frac{\var{by-ay}}{\var{bx-ax}} \\ \\ \var{bx-ax}(y - \var{ay}) &= \var{by-ay}(x - \var{ax})\\ \\ \simplify{{bx-ax}(y - {ay})} &= \simplify{{by-ay}(x - {ax})} \\ \\ \var{(bx-ax)}y - \var{(bx-ax)*ay} &= \var{(by-ay)}x + \var{(ay-by)*ax} \\ \\ \var{(bx-ax)}y &= \var{(by-ay)}x + \var{(ay-by)*ax+(bx-ax)*ay} \\ \\ y &= \simplify{({by-ay}/{bx-ax})x + {(ay-by)*ax/(bx-ax)+(bx-ax)*ay/(bx-ax)}} \end{split}$

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This question is used in the following exams:

Graphing by Ruth Hand in MASH Bath: Moodle quizzes and TS.
All the good stuff by Chris Templet in Chris's workspace.
Quiz 1 by Kate Vincent in Kate's workspace.
Scientific Maths Training Space by Ruth Hand in MASH Bath: Moodle quizzes and TS.
Psychology Maths Training Space by Ruth Hand in MASH Bath: Moodle quizzes and TS.
Straight Lines pre-A level by Ruth Hand in MASH Bath: Moodle quizzes and TS.
Bridging General Maths Quiz 2 by Kate Vincent in Kate's workspace.
Core Maths Test 2025 by Angus Rosenburgh in Angus's workspace.

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Linear graphs: Find the equation of a line 2

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

Christian Lawson-Perfect 2 years, 7 months ago

Ruth Hand 2 years, 9 months ago

Ruth Hand 3 years, 7 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Mathematical expression

Advanced settings

Checking accuracy

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Pattern restriction

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Error

Linear graphs: Find the equation of a line 2

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 2 years, 9 months ago

Ruth Hand 3 years, 7 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Mathematical expression

Advanced settings

Checking accuracy

Variable value generators

Pattern restriction

Variables

String restrictions

Generated value: `integer`