Direct proportionnotes

Unit 7: Direct Variation/Proportion ,[object Object],[object Object],[object Object]

Your Georgia Performance Standard: ,[object Object],[object Object]

IT / NOT IT ,[object Object],[object Object],[object Object],[object Object]

Direct Proportion also known as Direct Variation

Consider this: ,[object Object],[object Object],[object Object],$2.50, because every biscuit costs $2.50. # of biscuits times? =Total cost 1 2 5

Direct Proportion Defined: ,[object Object]

Direct Proportion ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],no – it is always $2.50 the # of biscuits

Direct Proportion: Equations ,[object Object],[object Object],[object Object],[object Object],Constant of Proportionality (AKA: unit rate)

What is the constant of proportionality for each of these equations? Direct Proportion : Equations IS a DIRECT VARIATION NOT! y = 3x y = 3x +1 y = x y = x-1 y = ½ x or y=x/2 y = x + 3 y = 1000000x y = 3/x

Direct Proportion : Graphs ,[object Object],[object Object],[object Object]

Direct Variation and its graph ,[object Object],[object Object],[object Object]

the ORIGIN!!!!! Special point known as the “ORIGIN” (0,0)

Tell if the following graph is a Direct Variation or not. No Yes No No

No Yes Yes No Tell if the following graph is a Direct Variation or not.

Let’s look again at the Frayer Diagram ,[object Object],[object Object],[object Object]

Homework tonight: ,[object Object]

Direct Proportion: Tables ,[object Object],[object Object]

direct proportion : the table ,[object Object],[object Object],[object Object],[object Object],People (x) Total Cost (y) 3 $30 5 $50 9 $90

Is it a Direct Proportion? Note, x increases: 6 , 7 , 8 and y increases: 12, 14, 16 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Yes! k = 10/20 or ½ k= 9/18 or ½ k= 7/14 or ½ k= 4/8 or ½ Equation? y = 1/2 x Is this a direct variation? If yes, give the constant of variation (k) and the equation.

No! The k values are different! Is this a direct variation? If yes, give the constant of variation (k) and the equation. k

Direct Proportion: Word Problems A car uses 8 gallons of gasoline to travel 280 miles. If the gas used and miles driven are proportional, how far will the car go on 10 gallons of gas? 25 gallons of gas? How many gallons are needed to drive 420 miles? ,[object Object],[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object],x gallons used y miles driven 8 280 10 350 25 875 12 420 k = y/x 280/8= 35 10 x 35 = 350 25 x 35 = 875 35x= 420 x=12

Frayer Diagram ,[object Object]

Direct proportionnotes

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