Question

Determine if the equations below are proportional or not proportional.

y = 2/3x + 4


y = 1/2x


2x + 3y = 7



Proportional because it crosses at the origin.


Not proportional because it does not cross at the origin.

Answer 1

1) y = 2/3x + 4, y is NOT PROPORTIONAL to x.

2) y = 1/2x , y is PROPORTIONAL to x.

3) 2x + 3y = 7 , y is NOT PROPORTIONAL to x.

Explanation:

Two quantities P and Q are said to be in proportion if one quantity is always a multiple of the other quantity.

or, P ∝ Q ⇒ P = k Q for some arbitrary constant k.

Here k = The Proportionality Constant.

Now, here

1) y = 2/3x + 4.

It is NOT of the form y = kx

Hence, y is NOT PROPORTIONAL to x.

2) y = 1/2x

Here, It is of the form y = kx where, k = 1/2 ( Proportional Constant)

Hence, y is PROPORTIONAL to x.

3) 2x + 3y = 7

or, y = 1/3( 7-2x)

It is NOT of the form y = kx

Hence, y is NOT PROPORTIONAL to x.

Answer 2

`y= (2)/(3) x + 4` is not proportional.

`y =(1)/(2) x` is proportional

2x + 3y = 7 is not proportional.

Explanation:

`y= (2)/(3) x + 4`.

This is an equation in the slope-intercept form and the y-intercept of the equation is (0,4).

Therefore, this equation does not pass through the origin.

So, the equation is not proportional.

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

This is also an equation in the slope-intercept form and the y-intercept of the equation is (0,0).

Therefore, this equation passes through the origin.

So, the equation is proportional.

2x + 3y = 7

⇒
`y = -(2)/(3) x + (7)/(3)`

This is also an equation in the slope-intercept form and the y-intercept of the equation is (
`0,(7)/(3)`).

Therefore, this equation does not pass through the origin.

So, the equation is not proportional.

(Answer)