Lesson 4 2 2 Proportional Relationships Graphs 7

Lesson 4. 2. 2 Proportional Relationships (Graphs) 7. RP. 2 a, 7. RP. 2 b

Prior Knowledge Who can tell me what the fancy word is for Unit Rate in proportional situations? Constant of Proportionality “K ”

Remember, on a graph… The independent variable appears on the x-axis. The dependent variable appears on the y-axis.

Today We are going to learn how to determine proportional relationships from a Graph. We are also going to learn how to find the Constant of Proportionality from a Graph. Before we get started… Let’s do an Exploration to see if you can determine the characteristics of a proportional graph!

Exploration Proportional Non-Proportional

Exploration Yes TABLE A TABLE B TABLE C Yes TABLE D Based on what you noticed about the proportional and nonproportional graphs on the previous slide… Can you pick out the 2 proportional graphs shown here? What makes you

Section 1 What makes a Graph Proportional?

Proportional Graphs The graph of a proportional relationship is a Straight-Line that passes through the origin (0, 0). Proportional Not Proportional

YOU TRY! Is the graph proportional or non-proportional? Why? 1)

YOU TRY! Is the graph proportional or non-proportional? Why? 2)

YOU TRY! Is the graph proportional or non-proportional? Why? 3)

YOU TRY! Is the graph proportional or non-proportional? Why? 4)

Section 2 How do you find the Constant of Proportionality from a Graph?

The graph shows the total cost in dollars, y, of purchasing x amount of concert tickets. • Is the relationship between number of tickets purchased and total cost proportional? Explain your reasoning. • How much do you think it costs to buy 1 concert ticket? Explain your reasoning? • Where can we place a dot on the line that would represent the cost of purchasing 1 concert ticket. • What x, y pair could be written that shows the cost of purchasing 1 ticket? ( 1, , 21 )

§ The rate for 1 of something is called the Unit Rate. § On the previous slide, the cost for 1 concert ticket was $21. § This value is also called the Constant of Proportionality. Let’s look at the steps for finding the Constant of Proportionality from a graph…

Finding the Constant of Proportionality from a Graph

YOU TRY! 1) 4 1 Y = 4 x

Finding the Constant of Proportionality from a Graph Notice that our previous technique would not work on this graph because the graphed line does not pass though a lattice point at the quantity of 1. We need different steps for this one! This means that the pool is filled with 5

Finding the Constant of Proportionality from a Graph Notice… Using the lattice point at (4, 20) would result in the same constant of proportionality.

YOU TRY! 2) (R) Rand is the money for South Africa.

YOU TRY! 3)

END OF POWERPOINT