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To determine the initial value and rate of change of the linear function, we can use the formula for the slope of a line, which is given by:
m = (y2 - y1) / (x2 - x1)
Taking the points (0,3) and (-3,4):
m = (3 - 4) / (0 - (-3))
m = -1 / 3
So the rate of change (or slope) of the linear function is -1/3.
Now we can use the point-slope form of a linear equation to find the initial value:
y - y1 = m(x - x1)
Using the point (0,3) and the rate of change -1/3:
y - 3 = (-1/3)(x - 0)
y - 3 = -1/3x
To simplify, we can rewrite the equation in slope-intercept form (y = mx + b):
y = -1/3x + 3
Therefore, the initial value of the linear function is 3.