what is the initial value and rate of change of (-3,4)(0,3)(3,2)(6,1)

Answer 1

To find the initial value and rate of change, we first need to determine the slope of the line that passes through the given points.

Using the formula for slope:
m = (y2 - y1) / (x2 - x1)

For the given points:
(-3,4) and (0,3)
m = (3 - 4) / (0 - (-3))
m = -1 / 3

(0,3) and (3,2)
m = (2 - 3) / (3 - 0)
m = -1 / 3

(3,2) and (6,1)
m = (1 - 2) / (6 - 3)
m = -1 / 3

Since the slope is constant for all three pairs of points, the initial value and rate of change can be determined using any of the points. Let's use the point (-3,4):

y = mx + b
4 = (-1/3)(-3) + b
4 = 1 + b
b = 3

Therefore, the initial value is 3 and the rate of change is -1/3.