Intercepts and gradients

Intercepts and gradients

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
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Further Resources
This task is about the gradient and intercepts on a graph.
Below is a graph of the function y = x - 1.

Graph of y = x - 1

graph of the function, y equals x minus 1
a)
What are the co-ordinates of the
 
 
i)
 
ii) 
x-intercept? (         ,         )
 
y-intercept? (         ,         )
 
b)
Calculate the gradient (or slope) of the line.
 
 
 
 
 
 
The gradient is __________
 
c)
 
On the graph above, plot the function: y = 3x
Task administration: 
This task is completed with pencil and paper only.
Level:
5
Curriculum info: 
Maths, Number and Algebra, Patterns and relationships
Keywords: 
co-ordinates, intercepts, plotting co-ordinates, slopes, linear equations, gradients
Description of task: 
Students identify the slope and intercepts of a linear equation, then plot a different function.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Patterns and relationships, sets 6-7
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
  Y10 (09/1998)
a) i)
ii)		 (1, 0)
(0, ⁻1)		 difficult
difficult
b)   1 [Accept m=1 or 1m or 1x] difficult
c)    All 6 points of y = 3x plotted accurately.
[Accept if accurate line drawn but no marked points].

 difficult
Diagnostic and formative information: 
   Student response Likely reason
a) i)
    ii)		 (8,7)
(9,8)		 Takes mid-point of x-axis and reads y co-ordinates.
Takes mid-point of y-axis and reads x co-ordinate.