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.

Today you will learn… To graph proportional relationships

Warm-Up

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.

On Your Own

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

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

On Your Own

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.

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

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.

Mini-Assessment

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

Homework pp. 586 – 587 1 – 17