PROPERTIES OF LINEAR FUNCTIONS (III)
Analysis
 
1. STRAIGHT LINES WITH A GRADIENT BETWEEN 0 AND 1 
We are going to see in which area of the plane we find straight lines whose gradient is between 0 and 1. 

y = m x
1.- Before we start, explain in your notebook where you think straight lines with a gradient between 0 and 1 are found on the plane .

 

Move the red point.

2.- Look carefully at the straight lines whose gradient is between 0 and 1. Write an explanation in your notebook.
2. STRAIGHT LINES WITH A GRADIENT OF MORE THAN 1. 
We are now going to see where lines with a gradient bigger than 1 are found on the plane.

y = m x
3.- Before you use the window try and guess where on the plane you think these lines are found and write it in your notebook.
 
Move the red point.

4.- Look carefully at what has happened and write an explanation in your notebook.

5.- Are there more straight lines in this activity or in the previous one?
3. GRADIENTS OF SYMMETRICAL STRAIGHT LINES
We are going to see what connection there is between the gradients of symmetrical straight lines.
Esta unidad interactiva requiere la máquina virtual de Java J2RE.
Move the red point on the blue line.

7.- Make the blue line go through the yellow points.

Move the red point on the orange line.

8.- Note that the symmetrical points of each point on the line, with respect to both axes, are found on the blue line.
9.- Compare linear functions that have opposite gradients 1 & -1; 2 & -2; 3.5 & -3.5, etc. What kind of symmetry do they have?
       
           
  Juan Madrigal Muga
 
Spanish Ministry of Education. Year 2001
 
 

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