Answer:
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 or
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.
<u><em>Verify each case</em></u>
case 1) we have
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
therefore
The equation not represent a a proportional relationship
case 2) we have
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
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
This is a linear equation expressed in the form
where
The constant of proportionality k or slope is equal to
For x=0, y=0
therefore
The equation represent a a proportional relationship