To solve this we have to set each value of x in the table in the function and see if we obtain the same y values:
y-6=-5/4 (x+2)
y= -5/4 (x+2)+6
x=-2
y= -5/4 (-2+2)+6
y=6
x=0
y= -5/4 (0+2)+6
y= -5/4 (2)+6
y= -5/2+6
y= 3.5
X=2
y= -5/4 (2+2)+6
y= -5/4 (4)+6
y= 1
x=4
y= -5/4 (4+2)+6
y= -5/4 (6)+6
y= -1.5
The first equation represents the data in the table
y-2=-5/4(x-1)
y= -5/4(x-1)+2
x=-2
y= -5/4(-2-1)+2
y=5.75 (it's not 6)
The second equation doesn't represent the data in the table
y+2=-5/4 (x-6)
y= -5/4 (x-6)-2
x=-2
y= -5/4 (-2-6)-2
y=8
The third equation doesn't represent the data in the table.
y-1= -5/4 (x-2)
y= -5/4(x-2)+1
x=-2
y= -5/4(-2-2)+1
y= 6
x=0
y= -5/4(0-2)+1
y= 3.5
x=2
y= -5/4(2-2)+1
y=1
x=4
y= -5/4(4-2)+1
y= -1.5
The fourth equation represents the data in the table
y-3.5 =-1.25x
y=-1.25x+3.5
x=-2
y=-1.25(-2)+3.5
y= 6
x=0
y=-1.25(0)+3.5
y=3.5
x=2
y=-1.25(2)+3.5
y=1
x=4
y=-1.25(4)+3.5
y= -1.5
The fifth equation represents the data in the table