# Graphing

3.1 Understanding Proportional Relationships (Extra Lesson)UNIT 3 • LESSON 1 UNDERSTANDING PROPORTIONAL RELATIONSHIPS adybug and ant move at constant speeds. The diagrams with tick marks show their positions at different times. Each tick mark represents 1 centimeter.  1. Lines uu and v also show the positions of the two bugs. Which line shows the ladybug’s movement? Which line shows the ant’s movement? Explain your reasoning.
2. How long does it take the ladybug to travel 12 cm? The ant?
3. Scale the vertical and horizontal axes by labeling each grid line with a number. You will need to use the time and distance information shown in the tick-mark diagrams.
4. Mark and label the point on line u and the point on line v that represent the time and position of each bug after travelling 1 cm.
Refer to the tick-mark diagrams and graph in the earlier activity when needed.
1. Imagine a bug that is moving twice as fast as the ladybug. On each tick-mark diagram, mark the position of this bug.
2. Plot this bug’s positions on the coordinate axes with lines uu and vv, and connect them with a line.
3. Write an equation for each of the three lines.
Here is a graph that could represent a variety of different situations. 1.  Write an equation for the graph.
2. Sketch a new graph of this relationship. You teacher will give you 12 graphs of proportional relationships.
1. Sort the graphs into groups based on what proportional relationship they represent.
2. Write an equation for each different proportional relationship you find.
Two large water tanks are filling with water. Tank A is not filled at a constant rate, and the relationship between its volume of water and time is graphed on each set of axes. Tank B is filled at a constant rate of 12 liters per minute. The relationship between its volume of water and time can be described by the equation v=12t, where t is the time in minutes and v is the total volume in liters of water in the tank. The graph of a very slight curve representing the volume of the tank in liters versus time in minutes The graph of a very slight curve representing the volume of the tank in liters versus time in minutes Sketch and label a graph of the relationship between the volume of water v and time t for Tank B on each of the axes. Answer the following questions and say which graph you used to find your answer. After 30 seconds, which tank has the most water? At approximately what times do both tanks have the same amount of water? At approximately what times do both tanks contain 1 liter of water? 20 liters?