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?

Question

asked Mar 25, 2022 126k views

1 Answer

Xorgate · Answer 1 · 2022-04-01T19:13:47+0000

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.