Answer:
[tex]y= \frac{2}{3} x + 4[/tex] is not proportional.
[tex]y =\frac{1}{2} x[/tex] is proportional
2x + 3y = 7 is not proportional.
Step-by-step explanation:
[tex]y= \frac{2}{3} x + 4[/tex].
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.
[tex]y =\frac{1}{2} x[/tex]
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
⇒ [tex]y = -\frac{2}{3} x + \frac{7}{3}[/tex]
This is also an equation in the slope-intercept form and the y-intercept of the equation is ([tex]0,\frac{7}{3}[/tex]).
Therefore, this equation does not pass through the origin.
So, the equation is not proportional.
(Answer)
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.
