1. Lesson 13.3 – Graphing Proportional Relationships
8.EE.5 – Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.
8.EE.6 – Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equations y = mx + b for a line intercepting the vertical axis at b.

2. Today you will learn…
To graph proportional relationships

3. Warm-Up

4. Key Idea Direct Variation
When two quantities x and y are proportional, the relationship can be represented by the direct variation equation y = mx, where m is the constant of proportionality.
The graph of y = mx is a line with a slope of m that passes through the origin.

7. On Your Own

8. Since the simplified ratios were equal,
Example 1: The following chart shows how much money Jordan earns for mowing lawns. Is the amount of money he earns proportional to the number of hours that he spends mowing?
Earnings ($)
Hours (h)
Unit Rate ( ) 14 1 28 2 42 3 56 4
Since the simplified ratios were equal,
this was a proportional relationship. 8

9. Let’s graph this proportional relationship from Ex. 1 on an xy-plane.
We typically put time (hours) on the x-axis, and the earnings ($) on the y-axis.
Set up the graph paper to fit the data in the chart.
Plot points (x, y) from the table. y
Hours (h)
Earnings ($)
Point (x, y) 1 14
(1, 14) 2 28
(2, 28) 3 42
(3, 42) 4 56
(4, 56) 56 42
Earnings ($) 28 14
Connect the points. x 1 2 3 4 5
Describe the graph of this
proportional relationship.
Hours worked

11. On Your Own

12. between cost and the number of tickets ordered.
Example 2: Ticket Express charges $7 per movie ticket plus a $3 processing fee per order. Is the cost of an order proportional to the number of tickets ordered? Explain .
Cost ($) 10 17 24 31
Tickets Ordered 1 2 3 4
Since all of the simplified ratios are not equal, there is NOT a proportional relationship
between cost and the number of tickets ordered.

13. Now, let’s graph this nonproportional relationship from Ex. 2.
Tickets ordered will be on the x-axis,
and the cost ($) will be on the y-axis. y
Plot points (x, y) from the table. 32
Tickets
Earnings ($)
Point (x, y) 1 10
(1, 10) 2 17
(2, 17) 3 24
(3, 24) 4 31
(4, 31) 28 24
Cost ($) 20 16 12 8 4
Connect the points. x
Describe the graph of this
nonproportional relationship. 1 2 3 4
Tickets ordered

14. nonproportional relationship. It is a straight line, but
This graph shows a
nonproportional relationship.
It is a straight line, but
it does not pass through the origin.

15. Mini-Assessment

16. “If a relationship is proportional, then…”
Please finish off this sentence.
Once finished, share with your partner what you stated.

17. Homework
pp. 586 – 587
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