# How can you use a graph to determine whether two rates are the same?

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How can you use a graph to determine whether two rates are the same?. For example: On Saturday, Jen walked 2.4 miles in 45 minutes. On Sunday, Jen walked 3.2 miles in 60 minutes. Did Jen walk at the same rate on Saturday and Sunday?. - PowerPoint PPT Presentation

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How can you use a graph to determine whether two rates are the same?For example:On Saturday, Jen walked 2.4 miles in 45 minutes. On Sunday, Jen walked 3.2 miles in 60 minutes. Did Jen walk at the same rate on Saturday and Sunday? 1In this lesson you will learn how to determine if two rates are equivalent by graphing.Read2 oranges

total fruit

=

oranges:total fruitapples

oranges

=

apples:oranges

Ratios

Lets ReviewI say, You already know what a ratio is. A ratio is a comparison between two quantities. If the quantities are the same, then you can have a part to whole ratio, such as oranges to all fruit, or a part to part ratio, like apples to oranges. If the quantities are different, then the ratio is referred to as a rate, such as miles to hours. In this lesson we will focus on rates. Notice how ratios can either be written as a fraction where one quantity is divided by the other, or with a colon between the two quantities.3(2,5)

(2,-5)

(-2,5)

(-2,-5)

yxLets ReviewHow to plot points4 (x,y)Up or down?Left or right?Positive xNegative xPositive yNegative yA Common Mistakex is always listed first and tells you the number of units to travel left or right. First go x units to the left of origin if x is negative and x units to the right if x is positive. Next, go y units up if y is positive and y units down if y is negative. 5Graphing Jens Walking Rate:

Let x = time spent walkingLet y = distance walked

Core LessonIf we let x = parts of yellow paint and y = parts of blue paint, then based on the within ratio, we can write an equation to determine the number of parts of blue paint based on the number of parts of yellow paint. 6Time(mins.)

Distance(miles)45

60

2.4

3.2

Distance (miles)Time (mins.)

Jens Walking Rate

65432100 15 30 45 60 (45,2.4)

(60,3.2)

Core LessonLearnZillion Notes:--The Core Lesson may take more than one slide. You can add as many of these slides as you like. Simply click on New Slide and then select the Core Lesson template slide to add a new one.--Feel free to move or resize the blue text box to fit your content.

7Time(hours)

Distance(miles)0.75

1

2.4

3.2

Distance (miles)Time (hours)

Jens Walking Rate

65432100 .25 .50 .75 1 (0.75,2.4)

(1,3.2)

Core LessonLearnZillion Notes:--The Core Lesson may take more than one slide. You can add as many of these slides as you like. Simply click on New Slide and then select the Core Lesson template slide to add a new one.--Feel free to move or resize the blue text box to fit your content.

8Graphs of Equivalent Rates:

Begin at the Origin

Form a Straight Line

Core LessonIf we let x = parts of yellow paint and y = parts of blue paint, then based on the within ratio, we can write an equation to determine the number of parts of blue paint based on the number of parts of yellow paint. 9In this lesson you have learned how to determine if two rates are equivalent by graphing.10 Let x = parts of yellow Let y = parts of blue Graph the data in the table to determine which green paint mixtures have equivalent ratios of x:y

PaintParts of YellowParts of BlueA12B23C36D46E58F69Guided Practice11Green Paint Mixtures BlueYellowA (1,2)B (2,3)C (3,6)D (4,6)F (6,9)E (5,8)Guided PracticeCompare Ratios of Parts Yellow : Parts Blue

A & C = 1:2

0

1

B, D & F = 2:3

0

1

E = 5:8

0

1

Guided PracticeCreate three shades of green paint by mixing different parts of yellow and green paint. Record the parts of yellow and green that you used in a table. Graph the data from your table. Write three equations for your green paint mixtures.Extension Activities14PaintParts of RedParts of YellowA20B42C33D36E01 Create the following paint mixtures. List the paints from the most red to the most yellow.Extension Activities15 Let x = parts of red y = parts of blue Graph the data in the table to determine which purple paint mixtures have the same ratio? PaintParts of RedParts of BlueA16B28C318D424E520F618Quick Quiz16