Direct and Inverse Variation Practice
Find the Missing Variable:
1) y varies directly with x. If y = -4 when x = 2, find y when x = -6.
2) y varies inversely with x. If y = 40 when x = 16, find x when y = -5.
3) y varies inversely with x. If y = 7 when x = -4, find y when x = 5.
4) y varies directly with x. If y = 15 when x = -18, find y when x = 1.6.
5) y varies directly with x. If y = 75 when x =25, find x when y = 25.
Classify the following as “direct”, “inverse”, or “neither” AND determine the constant of variation.
!
e
6) !! = ! −5!
7) c =
8)
=3
!
−4
9) ! =
!
!
12) ! = 4!
10) !! = !½!!
13) !" = ! −0.2
Answer the following questions.
14) If x and y vary directly, as x decreases, what happens to the value of y?
15) If x and y vary directly, as y increases, what happens to the value of x?
16) If x and y vary inversely, as x decreases, what happens to the value of y?
17) If x and y vary inversely, as y increases, what happens to the value of x?
11) !! = !
i
18
Write a complete sentence describing the relationship in the language of direct an inverse variation,
including the constant of variation/proportionality.
!!
1)
!=
2)
5 = !"
!
Write the equation represented by the information in the following sentences.
3)
The sales tax, T, is directly proportional to the purchase price, p, with the constant of proportionality
0.06
4)
Cost per person, C, varies inversely with number of members, n, with constant 225.
5)
The average speed for the Daytona 500 race is inversely proportional to the time it takes to complete
the race.
Example:
6)
Given the equation ! =
!
!.!"
answer the following questions:
i)
Is this function an example of direct variation, inverse variation, or neither? EXPLAIN!
ii)
What is the constant of variation/proportionality?
iii)
If C=150, find the value of I
iv)
If I = 67, find the value of C
v)
Express original equation in a different but EQUIVALENT SYMBOLIC FORM