Answer:
Please check the explanation.
Step-by-step explanation:
Given the function
[tex]y=\frac{3}{2}x\:+3[/tex]
- Putting all the values of y=9, 6, 0, and -3 to complete the table
FOR y=9
[tex]y=\frac{3}{2}x\:+3[/tex]
putting y=9
[tex]9=\frac{3}{2}x+3[/tex]
switch sides
[tex]\frac{3}{2}x+3=9[/tex]
subtract 3 from both sides
[tex]\frac{3}{2}x+3-3=9-3[/tex]
[tex]\frac{3}{2}x=6[/tex]
[tex]3x=12[/tex]
[tex]x=4[/tex]
Hence,
when y=9, x=4
FOR y=6
[tex]y=\frac{3}{2}x\:+3[/tex]
putting y=6
[tex]6=\frac{3}{2}x+3[/tex]
switch sides
[tex]\frac{3}{2}x+3=6[/tex]
subtract 3 from both sides
[tex]\frac{3}{2}x+3-3=6-3[/tex]
[tex]\frac{3}{2}x=3[/tex]
[tex]3x=6[/tex]
[tex]x=2[/tex]
Hence,
when y=6, x=2
FOR y=0
[tex]y=\frac{3}{2}x\:+3[/tex]
putting y=0
[tex]0=\frac{3}{2}x+3[/tex]
switch sides
[tex]\frac{3}{2}x+3=0[/tex]
subtract 3 from both sides
[tex]\frac{3}{2}x+3-3=0-3[/tex]
[tex]\frac{3}{2}x=-3[/tex]
[tex]3x=-6[/tex]
[tex]x=-2[/tex]
Hence,
when y=0, x=-2
FOR y=-3
[tex]y=\frac{3}{2}x\:+3[/tex]
putting y=-3
[tex]-3=\frac{3}{2}x+3[/tex]
switch sides
[tex]\frac{3}{2}x+3=-3[/tex]
subtract 3 from both sides
[tex]\frac{3}{2}x+3-3=-3-3[/tex]
[tex]\frac{3}{2}x=-6[/tex]
[tex]3x=-12[/tex]
[tex]x=-4[/tex]
Hence,
when y=-3, x=-4
Hence, the table becomes:
x y
9 4
6 2
0 -2
-3 -4
