Tasks | Early Adolescence | Investigating the Slope of a Line

Tasks - Years 10, 11 & 12

Investigating the Slope of a Line   by Thelma Perso, Senior Curriculum Officer Mathematics

Phase of Development:   Early Adolescence - Late Adolescence

Learning Area/s:	Mathematics
Strand/s	Substrand/s
Algebra	Understand Graphs Represent Variation
Working Mathematically	Apply and Verify Mathematical Strategies
Expected Outcomes:	Students understand the effect on a linear function and, in particular it's graph, in changing the coefficient of the independent variable.
Context:	Year 9,10, Foundations of Mathematics. I have used this investigation successfully with year 9 and 10 students, and with Foundations of Mathematics students.
Learning Activities/ Experience:	Students will work in pairs and individually to investigate linear functions.
Resources:	Graphics Calculators Worksheet

Worksheet

Investigating the Slope of a Line

1. Change the window of your calculator so that - 5 < x < 5 and - 5 < y < 5.

2. Draw y = 2/3 x. Sketch the graph.

   

3. Imagine you are a trace dot. Starting at the origin move in a positive x direction for 3 places and then in a positive y direction for 2 places. Where do you end up? Coordinates : x = _____ y =_____

4. Draw the triangle that you have 'produced' by this move. What sort of triangle is it?

   

5. Draw y = ¼ x. Sketch the graph.

   

6. Move along the x axis in a positive direction 4 places and then in a positive y direction 1 place. Is the triangle produced the same type?

7. Do you notice a pattern between the x coefficient and the 'rise' and 'run' of your triangles?

   

8. Draw y = 2/5 x and see what happens.

   What about y =

   1 3

   x and y - 2x

   ( Hint 2 =

   2 1

   )

9. In this table put the equations in order - from the smallest x coefficient to the largest, and draw a sketch of each graph.

   
   y = y = y = y =

10. Is there a relationship between the size of the coefficient and the steepness (or slope) of the line? Write about what you have noticed.

    

    

     

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    updated January 2002