Answer :
Answer:
[tex]y=\frac{1}{4}x[/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]k=\frac{y}{x}[/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.
Verify each case
case 1) we have
[tex]\frac{1}{4}x+y=10[/tex]
Remember that
In a proportional relationship the line passes through the origin
That means ----> For x=0, the value of y also must be zero
For x=0
[tex]\frac{1}{4}(0)+y=10\\\\y=10[/tex]
therefore
The equation not represent a a proportional relationship
case 2) we have
[tex]y=3x+7[/tex]
This is the equation of the line in slope intercept form
The y-intercept is b=7 ----> is not equal to zero
therefore
The equation not represent a a proportional relationship
case 3) we have
[tex]y=\frac{1}{3}x+1[/tex]
This is the equation of the line in slope intercept form
The y-intercept is b=1 ----> is not equal to zero
therefore
The equation not represent a a proportional relationship
case 4) we have
[tex]y=\frac{1}{4}x[/tex]
This is a linear equation expressed in the form [tex]y=kx[/tex]
where
The constant of proportionality k or slope is equal to
[tex]k=\frac{1}{4}[/tex]
For x=0, y=0
therefore
The equation represent a a proportional relationship