Question

Determine if the equations below are proportional or not proportional.

Answer 1

Answer:

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.

Step-by-step 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

Answer:

$y= \frac{2}{3} x + 4$ is not proportional.

$y =\frac{1}{2} x$ is proportional

2x + 3y = 7 is not proportional.

Step-by-step explanation:

$y= \frac{2}{3} x + 4$.  

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.

$y =\frac{1}{2} x$

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

⇒ $y = -\frac{2}{3} x + \frac{7}{3}$

This is also an equation in the slope-intercept form and the y-intercept of the equation is ($0,\frac{7}{3}$).

Therefore, this equation does not pass through the origin.

So, the equation is not proportional.

(Answer)