Question

If y is directly proportional to x and y=5 when x=2,find

(1) an equation connecting x and y
(2)the value of y when x =10
(3)the value of x when y=60

Answer 1

1)y=kx

2)5=K2

5/2=K2/2

k=2.5

when x=10

y=50

3)when y=60

x=12

Answer 2

see explanation

Explanation:

(1)

given y is directly proportional to x then the equation relating them is

y = kx ← k is the constant of proportionality

to find k substitute y = 5 when x = 2 into the equation

5 = 2k ( divide both sides by 2 )

2.5 = k

y = 2.5k ← equation connecting x and y

(2)

when x = 10 , substitute x = 10 into the equation

y = 2.5x = 2.5 × 10 = 25

(3)

when y = 60, substitute y = 60 into the equation

y = 2.5x , that is

60 = 2.5x ( divide both sides by 2.5 )

`(60)/(2.5)` = x , that is

x = 24