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 \(y/x=k\) or \(y=kx\)
In a linear direct variation the line passes through the origin and the constant of proportionality k is equal to the slope m
Let
\(A(0,0)\) ------> the line passes through the origin
\(B(2,10)\)
Find the value of k------> substitute the value of x and y
\(y/x=k\)-----> \(k=10/2=5\)
\(C(4,20)\)
Find the value of k------> substitute the value of x and y
\(y/x=k\)-----> \(k=20/4=5\)
\(D(6,30)\)
Find the value of k------> substitute the value of x and y
\(y/x=k\)-----> \(k=30/6=5\)
\(E(8,40)\)
Find the value of k------> substitute the value of x and y
\(y/x=k\)-----> \(k=40/8=5\)
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
\(f(x)=5x\)
