FUNCTIONS AND GRAPHS IV

Characteristics of linear functions

A common point

There is a point through which all straight lines that represent linear functions pass. 

1.- Change the slope and observe the commun point.

One point one straight line

Each point on a plane, different from the origin of co-ordinates, determines only one linear function.    

2.-Find the straight line that corresponds to the point A. (Move the orange point dragging with the mouse.)

Move the point A to the different quadrants and find the corresponding straight line.  Notice, in each case, the associated linear function.

Sign of the slope

The slope of a straight line can be positive, negative or zero.

3.- Is the slope of a linear function that passes through the point (4,6) positive or negative?

Answer the same question for (7,6); (-3,-4); (-5,9); (4,-8); (4,-100); (10,10); (-7,-7); (0,3); (0,-5).

Write in your book when the slope is positive, when it is negative and when it is zero.

Determination of the slope.

4.- Choose a linear function and check that the slope of the associated straight line is the quotient between the ordinate and the abscissa of any point on it different from the origin of co-ordinates.  (You can move the yellow point dragging with the mouse.)

m = y/x

Points that are not on the straight line.

5.- Check that the points which are outside the straight line have a quotient between its ordinate and abscissa different to the slope.  Test this with different straight lines. (You can move the yellow point dragging with the mouse.)

Sraight lines with a slope between 0 and 1

There is an area on the plane in which the slopes of the straight lines found on it have values between 0 and 1.

6.- Change the value of the slope between 0 and 1 and see what straight lines are obtained. 

Write the conclusions in your notebook.

Value of the slope greater than 1

7.- Change the value of the slope and see what straight lines have slopes greater than 1 .

Write the conclusions in your notebook.

Symmetries

8.- Compare the linear functions which have opposite slopes: 1 and -1; 2 and -2; 3,5 and -3,-5, etc. What symmetries do they present?

Author: Juan Madrigal Muga

	Ministerio de Educación, Cultura y Deporte. Año 2000