Plot the points (0,10), (1,8), (2,6), (3,4), (4,2).
What do you notice about the graph?
Read Graphs of Proportional Relationships.
The equation of a proportional relationship is of the form y = kx, where k is a positive number, and the graph is a line through (0, 0).
(1). Which of the relationships are proportional?
(2). What have you noticed about the graphs of proportional relationships? Do you think this will hold true for all graphs of proportional relationships?
(3). All the graphs in this activity show points where both coordinates are positive. Would it make sense for any of them to have one or more coordinates that are negative?
Match Tables and Graphs.
Plot Points from a Table of Proportional Relationships.
A lemonade recipe calls for cup of lemon juice for every cup of water.
(1.) What does represent?
(2.) What does represent?
(3.) Is there a proportional relation between and ?
(4.) Is there a proportional relationship between
The equation of a proportional relationship is of the form , where is a positive number, and the graph is a line through . What would the graph look like if were a negative number? You can use the applet below to explore this.
Move the red dot. When the scale factor k = 2, the area of the larger square is equal to 4 squares. Why when k = 3, the area is equal to 9 squares.
Which graphs could represent a proportional relationship?