Answer:
Part 11) The table represent a direct variation. The equation is [tex]y=18x[/tex]
Part 12) The table represent a direct variation. The equation is [tex]y=0.4x[/tex]
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
Part 11)
For x=0.5, y=9
Find the value of k
[tex]k=y/x[/tex] -----> [tex]k=9/0.5=18[/tex]
For x=3, y=54
Find the value of k
[tex]k=y/x[/tex] -----> [tex]k=54/3=18[/tex]
For x=-2, y=-36
Find the value of k
[tex]k=y/x[/tex] -----> [tex]k=-36/-2=18[/tex]
For x=1, y=18
Find the value of k
[tex]k=y/x[/tex] -----> [tex]k=18/1=18[/tex]
For x=-8, y=-144
Find the value of k
[tex]k=y/x[/tex] -----> [tex]k=-144/-8=18[/tex]
The values of k is the same for each ordered pair
therefore
The table represent a direct variation
The linear equation is
[tex]y=18x[/tex]
Part 12)
For x=-5, y=-2
Find the value of k
[tex]k=y/x[/tex] -----> [tex]k=-2/-5=2/5=0.40[/tex]
For x=3, y=1.2
Find the value of k
[tex]k=y/x[/tex] -----> [tex]k=1.2/3=0.40[/tex]
For x=-2, y=-0.8
Find the value of k
[tex]k=y/x[/tex] -----> [tex]k=-0.8/-2=0.4[/tex]
For x=10, y=4
Find the value of k
[tex]k=y/x[/tex] -----> [tex]k=4/10=0.4[/tex]
For x=20, y=8
Find the value of k
[tex]k=y/x[/tex] -----> [tex]k=8/20=0.4[/tex]
The values of k is the same for each ordered pair
therefore
The table represent a direct variation
The linear equation is
[tex]y=0.4x[/tex]
