Chp. 3.4 ­ Direct Variation
December 03, 2012
Date:
Chapter: Chapter 3:4 ­­> Direct Variation
Objectives: Solve, write, and graph direct variation equations.
Algebra I
Chp. 3.4 ­ Direct Variation
December 03, 2012
Notes:
*Direct Variation: y = kx where k cannot = 0 and is constant.
*Constant of Variation = aka Constant of Proportionality = k
= use k = y divided by x to find k
= slope!
Additional Info on Direct Variations
1) Always passes thru the origin (0, 0)
2) k>0 = positive slope
k<0 = negative slope
3) "y varies directly as x"
4) Most common direct variation is dirt! d=rt
"distance varies directly as time and r is the constant of variation"
Algebra I
Chp. 3.4 ­ Direct Variation
December 03, 2012
Examples:
Ex. 1 ­ Name the constant of variation then find the slope of the line that passes thru both points.
a) b)
Ex. 2 ­ Graph the direct variation.
a) y = (1/2)x
b) y = (3/4) x
Ex. 3 ­ Verbally explain how the graph would look.
a) y = 2x
b) y = x
c) y = (­3/2)x
d) y = ­3x
Ex. 4 ­ Write a direct variation equation that relates x and y if y varies directly as x.
a) y = 9, x = ­3
b) y = ­8, x = ­2
a1) y = ?, x = 2
b1) x = ?, y = 32
a2) x = ?, y = 15
c) y = 2, x = 4
c1) y = ?, x = ­6
Ex. 5
The Ramirez family is driving cross­country on vacation. They drive 330 miles in 5.5 hours. a) Write a direct variation equation that relates miles drive to hours
b) Graph
c) # hrs to drive 600 miles?
d) Slope? Meaning?
Ex. 6
Total cost (c) of bulk jelly beans is $4.49 times the number of pounds (p).
a) Write a direct variation equation that relates cost to pounds
b) Graph
c) Find cost for 3/4 lbs.
Ex. 7
Charles Law states that, at a constant pressure, volume of a gas (v) varies directly as its temperature (t). A volume of 4 cubic feet of a certain gas has a temperature of 2000. a) Write a direct variation equation that relates volume to temp.
b) Find the volume of the gas at 2500
Ex. 8
The cost of bananas varies directly with their weight. Michael bought 3 1/2 pounds for $1.12.
a) Write a direct variation equation that relates the cost of bananas to their weight.
b) Find the cost for 4 1/4 pounds.
Algebra I
Chp. 3.4 ­ Direct Variation
December 03, 2012
Homework:
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Algebra I