Answer:
The table not represent a proportional relationship
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 [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 origin
we have
For x=3, y=17
Find the value of k
[tex]k=y/x[/tex] -----> [tex]k=17/3=5.67[/tex]
For x=5, y=27
Find the value of k
[tex]k=y/x[/tex] -----> [tex]k=27/5=5.4[/tex]
For x=8, y=42
Find the value of k
[tex]k=y/x[/tex] -----> [tex]k=42/8=5.25[/tex]
For x=9, y=47
Find the value of k
[tex]k=y/x[/tex] -----> [tex]k=47/9=5.22[/tex]
The values of k are different
therefore
The table not represent a proportional relationship
Find the slope of the line
(3,17) and (9,47)
m=(47-17)/(9-3)=30/6=5
Find the equation of the line with m=5 and point (3,17)
y-y1=m(x-x1)
substitute
y-17=5(x-3)
y=5x-15+17
y=5x+2
This is the linear equation that represent the points in the table, but this equation not represent a proportional relationship (The line not passes through the origin)
