Answer:
Yes the table shows a proportional relationship between the variables x and y.
Step-by-step explanation:
Given : Table
[tex]x : \frac{1}{4}\ \ \frac{2}{4}\ \ \frac{3}{4} \\\\y : 3\ \ \ 6\ \ \ 9[/tex]
To find : Does the following table show a proportional relationship between the variables x and y.
Solution :
The proportional relationship between the variables x and y is given by,
[tex]y=kx[/tex]
Where, k is constant of proportionality
We substitute, [tex]x=\frac{1}{4}[/tex] and y=3
[tex]3=k(\frac{1}{4})[/tex]
[tex]k=3\times 4[/tex]
[tex]k=12[/tex]
So, The equation form is [tex]y=12x[/tex]
If rest points satisfy the equation then they are proportional.
Put [tex]x=\frac{2}{4}[/tex]
[tex]y=12\times \frac{2}{4}[/tex]
[tex]y=6[/tex]
True.
Put [tex]x=\frac{3}{4}[/tex]
[tex]y=12\times \frac{3}{4}[/tex]
[tex]y=9[/tex]
True.
Therefore, Yes the table shows a proportional relationship between the variables x and y.
