Question

the table represents some points on the graph of a liner function

x -2,2,4
y -11,17,20
which function represents this relationship
a) y=-3/2x+4
b)y=-3/4x-14
c)y=-2/3x-9
d)y=-2/3x-1

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine which function represents the relationship between x and y, we can substitute the given x-values and y-values into each of the options and see which one satisfies all three points.

For option a) y = -3/2x + 4:
- When x = -2: y = (-3/2)(-2) + 4 = 3 + 4 = 7
- When x = 2: y = (-3/2)(2) + 4 = -3 + 4 = 1
- When x = 4: y = (-3/2)(4) + 4 = -6 + 4 = -2

Since none of these y-values match the given y-values in the table (-11, 17, 20), option a) does not represent the relationship.

For option b) y = -3/4x - 14:
- When x = -2: y = (-3/4)(-2) - 14 = 1.5 - 14 = -12.5
- When x = 2: y = (-3/4)(2) - 14 = -1.5 - 14 = -15.5
- When x = 4: y = (-3/4)(4) - 14 = -3 - 14 = -17

Again, none of these y-values match the given y-values in the table, so option b) does not represent the relationship.

For option c) y = -2/3x - 9:
- When x = -2: y = (-2/3)(-2) - 9 = 4/3 - 9 = -23/3
- When x = 2: y = (-2/3)(2) - 9 = -4/3 - 9 = -31/3
- When x = 4: y = (-2/3)(4) - 9 = -8/3 - 9 = -35/3

Once again, none of these y-values match the given y-values in the table, so option c) does not represent the relationship.

Finally, for option d) y = -2/3x - 1:
- When x = -2: y = (-2/3)(-2) - 1 = 4/3 - 1 = 1/3
- When x = 2: y = (-2/3)(2) - 1 = -4/3 - 1 = -7/3
- When x = 4: y = (-2/3)(4) - 1 = -8/3 - 1 = -11/3

The y-values (-11/3, 17/3, 20/3) in option d) match exactly with the given y-values in the table (-11, 17, 20). Therefore, the correct function that represents the relationship is option d) y = -2/3x - 1.