Question

The tables below show the values of Y for different values of X

Answer 1

Option D

Explanation:

Rate of change of a linear function between two points
`(x_1,y_1)` and
`(x_2,y_2)` is given by,

Rate of change 'm' =
`(y_2-y_1)/(x_2-x_1)`

From the given table,

Rate of change of the function between (-2, 6) and (-4, 9),

Rate of change 'm' =
`(9-6)/(-4-(-2))`

m =
`(3)/(-2)`

Initial value = y-intercept

Let the equation of the line passing through a point (h, k) is,

y - k = m(x - h)

If a point (-2, 6) is lying on the graph of the function,

y - 6 =
`-(3)/(2)(x+2)`

y =
`-(3)/(2)x-3+6`

y =
`-(3)/(2)x+3`

Y-intercept of the function = 3

Therefore, initial value of the function = 3

Option D is the answer.