Question

Which table shows y as DIRECTLY PROPORTIONAL to x?

A) A

B) B

C) C

D) D
graphs:

24)
A
x y
1 1
2 4
3 9
4 16
C
x y
1 4
2 2
3 4/3
4 1
B
x y
1 1/2
2 1
3 3/2
4 2
D
x y
1 3
2 5
3 7
4 9

Answer 1

Option B gives the directly proportional relation.

Step-by-step explanation:

If a function can be written as in the form y = kx ........... (1), where x is the independent variable, y is the dependent variable and k is the proportionality constant.

Now, from the given four tables in options, the table in option B only satisfies this relation between x and y.

The ordered pairs in the option B are (1,0.5), (2,1), (3,1.5) and (4,2).

Now, take any two pairs of coordinates and find the equation of the function that satisfies all four points.

Taking (1,0.5) and (2,1) points, the equation of the straight line will be

`(y - 1)/(1 - 0.5) = (x - 2)/(2 - 1)`

⇒ 2(y - 1) = x - 2

⇒ 2y = x

⇒
`y = (1)/(2) x` ............. (2)

Therefore, this equation (2) is similar to equation (1) and hence this table is directly proportional relationship. (Answer)