Question
what is the initial value and rate of change of (-3,4)(0,3)(3,2)(6,1)
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Answered by
GPT 3.5
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.
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.
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