To determine the initial value and rate of change of the linear function from the given points (-3, 4), (0, 3), (3, 2), and (6, 1), we can use the formula for the equation of a line:
y = mx + b
where m is the rate of change (slope) and b is the initial value (y-intercept).
First, calculate the rate of change (m) using two points:
m = (y2 - y1) / (x2 - x1)
m = (2 - 3) / (3 - 0)
m = -1 / 3
m = -0.333
Next, choose one of the points to substitute the values of m and solve for b:
Using point (3, 2):
2 = (-0.333)(3) + b
2 = -1 + b
b = 3
Therefore, the initial value is 3 and the rate of change is -0.333.
Image to Text%0D%0A(-3, 4)%0D%0A(0, 3)%0D%0A(3, 2)%0D%0A(6, 1)%0D%0Ax%0D%0Ay%0D%0ASummary%0D%0AThe image shows a Cartesian plane with an x-axis and a y-axis. On this plane, there is a line with four distinct points labeled. These points are plotted as follows: (-3, 4), (0, 3), (3, 2), and (6, 1). The line passes through all these points, suggesting they are collinear and indicating a negative linear relationship between the x and y values; as x increases, y decreases. This could represent a linear function or data trend in a graph. Determine the initial value and the rate of change of the linear function as given in the graph. Round the answer to three decimal places as needed.%0D%0A%0D%0A(1 point)%0D%0AThe initial value is , and the rate of change is .
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