To determine which equation represents the data, we can substitute the given values of x and y into each equation and see which equation satisfies all the points.
1) For the equation Y= -3/2x+4:
For x = -2, Y = (-3/2)(-2) + 4 = 6
For x = 2, Y = (-3/2)(2) + 4 = 1
For x = 4, Y = (-3/2)(4) + 4 = -2
This equation does not satisfy the second point (2, -17).
2) For the equation Y= -3/2x-14:
For x = -2, Y = (-3/2)(-2) - 14 = -11
For x = 2, Y = (-3/2)(2) - 14 = -17
For x = 4, Y = (-3/2)(4) - 14 = -20
This equation satisfies all the given points.
3) For the equation Y= -2/3x-9:
For x = -2, Y = (-2/3)(-2) - 9 = -7.33
For x = 2, Y = (-2/3)(2) - 9 = -8.67
For x = 4, Y = (-2/3)(4) - 9 = -10.33
This equation does not satisfy the first point (-2, -11).
4) For the equation Y= -2/3x-1:
For x = -2, Y = (-2/3)(-2) - 1 = 1.33
For x = 2, Y = (-2/3)(2) - 1 = -2.33
For x = 4, Y = (-2/3)(4) - 1 = -6.33
This equation does not satisfy the second point (2, -17).
Therefore, the equation that represents the given data is Y= -3/2x-14.
X Y
-2. -11
2. -17
4. -20
Y= -3/2x+4
Y= -3/2x-14
Y= -2/3x-9
Y= -2/3x-1
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