Question

Line KJ represents a proportional relationship. Point K lies at (12,14) as shown on the graph below.

Which ordered pair could represent the coordinates of point J?

Answer 1

Given:

Line KJ represents a proportional relationship.

Point K lies at (12,14).

To find:

The ordered pair of the coordinates of point J.

Solution:

If y is proportional to x, then

`y\propto x`

`y=kx`

`(y)/(x)=k`

Where, k is the constant of proportionality.

It means, the ratios of y to x for all the point in a proportional relationship are same.

Line KJ represents a proportional relationship. Point K lies at (12,14).

So, the constant of proportionality is:

`k=(14)/(12)`

`k=(7)/(6)`

Similarly, find the ratio of y to x for all given points.

In option a,

`(3.5)/(3)=(3.5* 2)/(3* 2)`

`(3.5)/(3)=(7)/(6)`

In option b,

`(15)/(17.5)=(15* 2)/(17.5* 2)`

`(15)/(17.5)=(30)/(35)`

`(15)/(17.5)=(6)/(7)`

In option c,

`(0)/(2)=0`

In option d,

`(3)/(3.5)=(3* 2)/(3.5* 2)`

`(3)/(3.5)=(6)/(7)`

The ratio of y to x of point (3,3.5) is equal to the ratio of given point K(12,14). So, the coordinates of point J are (3,3.5).

Therefore, the correct option is A.