Tasks | Early Adolescence | Investigating Straight Lines

Tasks - Year 9, 10

Investigating Straight Lines   by Thelma Perso, Senior Curriculum Officer

Phase of Development:   Early Adolescence

Learning Area/s:	Mathematics
Strand/s	Substrand/s
Algebra	Understand Graphs Represent Variation Understand Symbols
Working Mathematically	Mathematical Strategies Apply and Verify
Expected Outcomes:	Students understand the relationship between the value of 'c' and the graph of a linear function y = mx + c.
Context:	I have used this investigation successfully with year 10 students.
Learning Activities/ Experience:	Assumed Knowledge Students use their graphics calculator to give them immediate visual feedback on the affect of changing the value of the constant added to a linear equation. (An extension may be to investigate the effect of changing the value of c on the graph of y = ax2 + bx + c or y = sin x + c y = cos x + c y = 2x + c ...etc)
Resources:	Graphics Calculator Worksheet

Worksheet

Investigating Straight Lines

1. Use your function grapher to graph the curve y = x. draw a sketch in the box below
[Y₁ = X]

2. Now draw the graph of y = x + 1 on the same axis [Y2 = X + 1] - it may be easier to notice the difference between these curves if you change the scale and the max / min values in your display.

• What is the y intercept for y = x +1?

  

• Draw a sketch of y = x + 1 on the diagram above.

3. Now draw the graph of y = x + 2 using you function grapher (Y3 = X+ 2). Sketch this above.

• What is the y intercept for y = x + 2?

  

• What is the y intercept for y = x + 2?

  

• What is it ?

  

7. Write about what you notice.

8. Can you predict the Y intercept for the curves?

Y = x + 7		Check these using your function grapher
Y = x - 2
Y = x + 2.7

9. Try to generalise your results ie. what happens to the graph of y = x + k if k is any number?