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?
In this lesson you will learn how to determine if two rates are equivalent by graphing.
Let’s Review oranges total fruit = oranges:total fruit apples oranges = apples:oranges Ratios
(2,5) (2,-5) (-2,5) (-2,-5) y x
A Common Mistake (x,y) Up or down? Left or right? Positive x Negative x Positive y Negative y
Core Lesson Graphing Jen’s Walking Rate: Let x = time spent walking Let y = distance walked
Time (mins.) Distance (miles) Distance (miles) Time (mins.) Jen’s Walking Rate (45,2.4) (60,3.2)
Core Lesson Time (hours) Distance (miles) Distance (miles) Time (hours) Jen’s Walking Rate (0.75,2.4) (1,3.2)
Core Lesson Graphs of Equivalent Rates: BBegin at the Origin FForm a Straight Line
In this lesson you have learned how to determine if two rates are equivalent by graphing.
Guided Practice 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 Blue A12 B23 C36 D46 E58 F69
Guided Practice Green Paint Mixtures Blue Yellow A (1,2) B (2,3) C (3,6) D (4,6) F (6,9) E (5,8)
Guided Practice Compare Ratios of Parts Yellow : Parts Blue A & C = 1:2 0 1 B, D & F = 2:3 0 1 E = 5:8 0 1
Extension Activities Create 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.
PaintParts of RedParts of Yellow A20 B42 C33 D36 E01 Create the following paint mixtures. List the paints from the most red to the most yellow.
Quick Quiz 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 Blue A16 B28 C318 D424 E520 F618