Proportional Relationships

Slides:

Advertisements

Similar presentations

Proportional Relationships

Advertisements

5 Minute Check Find the function rule and the value of the 12th term. Complete in your notebook Position(n) Value of Term Position(n)

Today, we will graph the information from the tables of values that we worked with yesterday in class. Our objective is to use a graph to identify if a.

5 Minute Check Complete in your notes. MegaMart collects a sakes tax equal to 1/16 of the retail price of each purchase. The tax is sent to the government.

5 Minute Check Complete in your notes mi/h = ? ft/min 2. 16cm/min = ? m/h mi/h = ? ft/s 4. 26cm/s = ? m/min You can use your calculator for.

Identifying and Representing Proportional Relationships

Topic A: Proportional Relationships

Constant of Proportionality

Graphing. Representing numerical information in a picture. Graph shows a picture of a relationship -how two processes relate -what happens when two events.

Constant of Proportionality

 A constant ratio in any proportional relationship  Really just another name for unit rate! Remember, to be constant means it never changes!

 A constant ratio in any proportional relationship  Really just another name for unit rate! Remember, to be constant means it never changes!

Proportions. An equation stating that two ratios are equivalent is called a proportion. 200 Miles 4 Hours 50 Miles 1 Hour = An equation stating that two.

Graph proportional relationships

Determining Slope and Y-Intercept

Lesson 2-3 Example Graph the ordered pairs C(2, 5) and D(0, 5). Then connect the points. What do you notice? Step 1 Graph point C. Start at the origin,

Notes - Coordinate Plane & Graphing Quiz

Splash Screen. Over Lesson 6–3 5-Minute Check 1 Using the points in the table, graph the line. Determine whether the set of numbers in each table is proportional.

Slide 1 Lesson 76 Graphing with Rates Chapter 14 Lesson 76 RR.7Understand that multiplication by rates and ratios can be used to transform an input into.

3.6 – Proportional & Nonproportional Relationships

Topic 1 Ratios and Proportional Relationships. Lesson Rates A ratio that compares two quantities with different kinds of units is called a rate.

Proportional vs. Non-Proportional If two quantities are proportional, then they have a constant ratio. –To have a constant ratio means two quantities.

5 Minute Check Complete in your notes. MegaMart collects a sakes tax equal to 1/16 of the retail price of each purchase. The tax is sent to the government.

Graph Proportional Relationships. x y –2 2 2 –4 4 4 –1 –3 – –3 –5 –1 Origin x-axis y-axis back.

S ECTION 1.4 P ROPORTIONAL AND NONPROPORTIONAL RELATIONSHIPS EQ: How do I determine a proportional relationship?

P ATTERNS AND P ROPORTIONAL R ELATIONSHIPS. D IRECT P ROPORTION The table below is a linear function. X1234 Y One way to describe the function.

Course 2, Lesson The amount a cashier earns is shown in the table. Determine whether the amount earned is proportional to the number of hours worked.

Graphing proportional

Solve each equation for y. 1. 3x + y = 52. y – 2x = x – y = x + 4y = 85. 9y + 3x = 16. 5y – 2x = 4 Clear each equation of decimals x.

What is best? 20oz popcorn for $4.50 or 32 oz popcorn for $7.00 ? $ 4.50 / 20 = $0.225 per oz so $0.23 Here is the Unit Cost: $7.00 / 32 = $ per.

PO D Wawa charges $7.50 for 3 packs of Trident. Find the unit rate.

Sample Project.  Find the unit rate for each set of data in the table.  If the unit rates are the same for each entry, then the relationship is proportional.

LESSON 5: Identifying Proportional and Non-Proportional Relationships in Graphs Dr. Basta Isaiah sold candy bars to help raise money for his.

ALGEBRA READINESS LESSON 8-6 Warm Up Lesson 8-6 Warm-Up.

1.A 2.B 3.C 4.D 5Min 7-3 Triangle XYZ has vertices X(2, 2), Y(10, 4), and Z(8, 10). Find the vertices of triangle XYZ after a dilation with a scale factor.

Constant of Proportionality. A direct variation is represented by a ratio or equation : or k ≠ 0 Direct Variation – constant ratio EX1) Determine if the.

5 Minute Check. Simplify Minute Check.

P ROPORTIONALITY USING G RAPHS AND T ABLES February 2013.

Proportional and Non-proportional Relationships. An equation stating that two ratios are equivalent is called a proportional. 200 Miles 4 Hours 50 Miles.

Constant of Proportionality. A direct variation is represented by a ratio or equation : or k ≠ 0 Direct Variation – constant ratio EX1) Determine if the.

+ Directly Proportional. + Directly proportional: as one amount increases, another amount increases at the same rate. Hence, the straight line when we.

Representing Proportional Relationships 8.EE.5 - GRAPH PROPORTIONAL RELATIONSHIPS, INTERPRETING THE UNIT RATE AS THE SLOPE OF THE GRAPH. COMPARE TWO DIFFERENT.

Identifying a Proportional Relationship A.) Proportional relationships and charts B.) Proportional relationships and graphs D.) Explaining the x and y.

Topic A: Proportional Relationships

Determine the relationship between the sets: Set 1Set Set 1Set Set 1Set Set 1Set

Proportionality using Graphs and Tables

Constant Rate of Change

Warm-up October 24, 2016 Complete Monday’s Weekly Basics problems

Lesson 13.3 – Graphing Proportional Relationships

Proportional Relationships

DIRECT VARIATIONS.

1.4 Proportional and Non proportional Relationships

Constant of Proportionality

Proportional and Nonproportional Relationships

Lesson 4.3 Graphing Proportional Relationships

Constant Rate of change

Lesson 7.9 Identifying Proportional Relationships

FACTOR: 6D + 6 5T – 5 4D + 8 3F – 9 8G + 10 Turn in page 275

FACTOR: 6D + 6 5T – 5 4D + 8 3F – 9 8G H – 6 5K + 5M + 25

Proportional Relationships

Bell-work 9/29/16 Triangle XYZ has vertices X(2, 2), Y(10, 4), and Z(8, 10). Find the vertices of triangle X’Y’Z’ after a dilation with a scale factor.

Recall that a proportional relationship is a relationship between two quantities in which the ratio of one quantity to the.

Proportional Relationships

Proportionality using Graphs and Tables

Main Idea and New Vocabulary

x − 7 = 13 m − 9 = −13 m + 4 = −12 Ticket in the Door

5.5 Proportional and Nonproportional relationships

Proportional or Non-proportional?

x − 7 = 13 m − 9 = −13 m + 4 = −12 Ticket in the Door

Agenda Ticket in the Door Review of ticket in the Door

Presentation transcript:

Proportional Relationships 4/21/2017 Identifying Proportional Relationships From graphs Today, we will graph the information from the tables of values that we worked with yesterday in class. Our objective is to use a graph to identify if a relationship is proportional or not.

Since the simplified ratios were equal, 4/21/2017 Example 1: The following chart shows how much money Alex 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.

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

The graph of a proportional relationship: is a straight line, AND it passes through the origin, or point (0,0).

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.