Respuesta :

calculista

Answer:

Option A

[tex]1/2[/tex]

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

so

For [tex]x=2, y=1[/tex]

[tex]k=y/x=1/2[/tex]

For [tex]x=4, y=2[/tex]

[tex]k=2/4=1/2[/tex]

For [tex]x=6, y=3[/tex]

[tex]k=3/6=1/2[/tex]

For [tex]x=8, y=4[/tex]

[tex]k=4/8=1/2[/tex]

Answer:

Option A is correct

[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Direct proportionality states:

if [tex]y \propto x[/tex]

then, the equation is in the form of:

[tex]y = kx[/tex] ......[1] where, k is the constant of proportionality.

As per the statement:

Consider any points from the given table:

Let (x, y) = (4, 2)

Substitute these points in [1] we have;

[tex]2 = 4k[/tex]

Divide both sides by 4 we have;

[tex]\frac{1}{2} = k[/tex]

or

[tex]k=\frac{1}{2}[/tex]

Therefore, the constant of proportionality for the relationship is, [tex]\frac{1}{2}[/tex]