Answer:
The function represents a direct variation
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]
In a linear direct variation the line passes through the origin and the constant of proportionality k is equal to the slope m
Let
[tex]A(0,0)[/tex] ------> the line passes through the origin
[tex]B(2,10)[/tex]
Find the value of k------> substitute the value of x and y
[tex]y/x=k[/tex]-----> [tex]k=10/2=5[/tex]
[tex]C(4,20)[/tex]
Find the value of k------> substitute the value of x and y
[tex]y/x=k[/tex]-----> [tex]k=20/4=5[/tex]
[tex]D(6,30)[/tex]
Find the value of k------> substitute the value of x and y
[tex]y/x=k[/tex]-----> [tex]k=30/6=5[/tex]
[tex]E(8,40)[/tex]
Find the value of k------> substitute the value of x and y
[tex]y/x=k[/tex]-----> [tex]k=40/8=5[/tex]
The value of k is equal in all the points of the table and the line passes through the origin
therefore
The function represents a direct variation
the equation of the direct variation is equal to
[tex]f(x)=5x[/tex]
