The table below shows the values of y for different values of x:x y0015210315Which equation shows the relationship between x and y?

Accepted Solution

Answer:[tex]y=5x[/tex]Step-by-step explanation:we know thatA relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/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 originwe haveFor x=0, y=0 -----> the line passes through the originFor x=1, y=5 ----> [tex]k=y/x=5/1=5[/tex]For x=2, y=10 ----> [tex]k=y/x=10/2=5[/tex]For x=3, y=15 ----> [tex]k=y/x=15/3=5[/tex]soThe constant of proportionality is k=5The table represent a direct variationThe equation is equal to [tex]y=kx[/tex]substitute the value of k[tex]y=5x[/tex]