Direct variation describes the relationship between two quantities where they are in a constant ratio. If x is directly proportional to y, their relationship can be written as y = kx, where k is the constant of proportionality. Several examples are provided to demonstrate calculating the constant of proportionality given initial values of x and y, and then using the relationship to find corresponding values of y when given new values of x, and vice versa.

1. Direct variation

3. a) If two varying quantities are always in the same
ratio, they are said to be directly proportional to one
another.
x y
If is directly proportional , then this
kxy x y 
can be written as or where k
is a constant.

4. x y 7y x
 A) . If ,when =2,find when
=5
x
y kx
7  
2
 
k
 When =5
3.5
7
2
  
3.5 5 17.5

y
k
y
x

6. . x y6y x
Q1) , if when =2, Find
a) The constant of proportionality
b) The value of y
,when x =7
c) The value of , when =9
d) The value of , when =9
x y
x y

7. . 2 x y  18  y x
, if when =6, Find
a) The constant of proportionality
b) The value of y
,when x =4
c) The value of x , when y
=32

8. . x y8y x
Q1) , if when =2, Find
a) The constant of proportionality
b) The value of y
,when x =4
c) The value of , when =12
d) The value of , when =6
x y
x y