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McGraw Hill Glencoe Algebra 1, 2012

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McGraw Hill Glencoe Algebra 1, 2012 View details

7. Inverse Linear Functions

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Exercise 54 Page 270

What is the form of a direct variation equation?

-4.4

Practice makes perfect

Functions where y varies directly with x — direct variation equations — follow a specific format. y=mx In this form, m≠ 0. By substituting the given values for x and y into the equation, we can determine the constant of variation, m.

y=mx

x= 9.9, y= -6.6

-6.6=m* 9.9

▼

Solve for m

Rearrange equation

m * 9.9 =-6.6

LHS * 10=RHS* 10

m * 9.9 * 10=-6.6 * 10

Multiply

99m=-66

.LHS /99.=.RHS /99.

99m/99=-66/99

MovePartNumRight

a* b/c=a/c* b

99/99 * m=-66/99

a/a=1

1 * m=-66/99

Identity Property of Multiplication

m=-66/99

MoveNegNumToFrac

Put minus sign in front of fraction

m=-66/99

a/b=.a /33./.b /33.

m=-66/ 33/99/ 33

Calculate quotient

m=-2/3

Now that we know that the constant of variation is - 23, we can write the function. y= -2/3x Finally, by substituting x=6.6 into the function, we can find the corresponding y-value.

y=-2/3x

x= 6.6

y=-2/3* 6.6

▼

Simplify RHS

MoveRightFacToNum

a/c* b = a* b/c

y=-2*6.6/3

Multiply

y=-13.2/3

Calculate quotient

y=-4.4

For the equation y=- 23x, when x=6.6, the value of y is -4.4.

Subchapter links

Check Your Understanding p.267

Practice and Problem Solving p.267-269

H.O.T. Problems p.269

Standardized Test Practice p.270

Spiral Review p.270

Skills Review p.270