ACTIVITIES WITH LINEAR FUNCTIONS  
Analysis  
1. CHOOSING THE GRADIENT  
The gradient of a straight line depends on the coordinates of the points it passes through.  y = m x 

1. Click on the Start button (init) to change the points to 0. Choose the number that corresponds to the gradient of the orange straight line by looking carefully at the coordinates of the green point on the line.


2. Repeat the process until you get 10 points. 
2. GUESSING THE GRADIENT  
We need to find a method that allows us to guess the gradient of a linear function by reading its graph.  y = m x 

3. Find the gradient of the orange line. First locate the green point and look at its coordinates.
4. Repeat the process until you get 10 points. 5. In your notebook explain how we can obtain the gradient of a line that passes through a given point. 
3. ESTIMATING THE GRADIENT  
Now we need to know how to estimate the gradient of any straight line.  y = m x 

6. Estimate the gradient of the orange line.
7. Repeat the process until you get 10 points. 
4. THE ANGLE BETWEEN A STRAIGHT LINE AND THE SEMIAXIS OX.  
The angle formed by a straight line and the semiaxis OX (positive coordinates along the xaxis) is connected to its gradient. The gradient of the line is the same as the tangent of this angle formed by the straight line and the semiaxis OX.  y = m x 

8. Look carefully at the values given for the angle formed with different straight lines in each quadrant.
9. Write down the gradients of the straight lines for the following angles:

Juan Madrigal Muga  
Spanish Ministry of Education. Year 2001  
Except where otherwise noted, this work is licensed under a Creative Common License