# ﻿Introducing Graphs of Proportional Relationships

Warmup

Plot the points (0,10), (1,8), (2,6), (3,4), (4,2).

What do you notice about the graph?

Activity #1

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).

• You can use the applet below to find out what the graph will look like if k were a negative number..
• Match each table below with the corresponding graph. You can use the scroll wheel on your mouse to zoom in.

(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?

Activity #2

Match Tables and Graphs.

• Match each table with the corresponding graph.

Activity #3

Plot Points from a Table of Proportional Relationships.

A lemonade recipe calls for cup of lemon juice for every cup of water.

• Use the table below to answer the following questions.

(1.) What does represent?

(2.) What does represent?

(3.) Is there a proportional relation between and ?

(4.) Is there a proportional relationship between

• Plot the pairs in the table in the coordinate plane below.

Challenge #1

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.

Challenge #2

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.

Challenge #3

Which graphs could represent a proportional relationship?

Quiz Time