Answer:
Option D
Step-by-step explanation:
Rate of change of a linear function between two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by,
Rate of change 'm' = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
From the given table,
Rate of change of the function between (-2, 6) and (-4, 9),
Rate of change 'm' = [tex]\frac{9-6}{-4-(-2)}[/tex]
m = [tex]\frac{3}{-2}[/tex]
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 = [tex]-\frac{3}{2}(x+2)[/tex]
y = [tex]-\frac{3}{2}x-3+6[/tex]
y = [tex]-\frac{3}{2}x+3[/tex]
Y-intercept of the function = 3
Therefore, initial value of the function = 3
Option D is the answer.
