Answer:
Option D
Step-by-step explanation:
Rate of change of a linear function between two points
and
is given by,
Rate of change 'm' = ![\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
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)}](https://tex.z-dn.net/?f=%5Cfrac%7B9-6%7D%7B-4-%28-2%29%7D)
m = ![\frac{3}{-2}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B-2%7D)
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)](https://tex.z-dn.net/?f=-%5Cfrac%7B3%7D%7B2%7D%28x%2B2%29)
y = ![-\frac{3}{2}x-3+6](https://tex.z-dn.net/?f=-%5Cfrac%7B3%7D%7B2%7Dx-3%2B6)
y = ![-\frac{3}{2}x+3](https://tex.z-dn.net/?f=-%5Cfrac%7B3%7D%7B2%7Dx%2B3)
Y-intercept of the function = 3
Therefore, initial value of the function = 3
Option D is the answer.