Question

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

Answer 1

Answer:

Option D

Step-by-step 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' = $\frac{y_2-y_1}{x_2-x_1}$

From the given table,

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

Rate of change 'm' = $\frac{9-6}{-4-(-2)}$

                           m = $\frac{3}{-2}$

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 = $-\frac{3}{2}(x+2)$

y = $-\frac{3}{2}x-3+6$

y = $-\frac{3}{2}x+3$

Y-intercept of the function = 3

Therefore, initial value of the function = 3

Option D is the answer.