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.
(1 point)
The points on the graph are
(-3,4)
(0,3)
(3,2)
(6,1)
The initial value is___and the rate of change is___
To find the initial value of the linear function, we need to find the y-intercept, which is the y-coordinate when x=0. From the given points, we can see that when x=0, y=3. Therefore, the initial value is 3.
To find the rate of change of the linear function, we need to find the slope of the line. The slope is determined by the change in y divided by the change in x. We can choose any two points on the line to calculate the slope. Let's choose the points (0,3) and (6,1).
Change in x = 6-0 = 6
Change in y = 1-3 = -2
Slope = change in y / change in x = -2/6 = -1/3
Therefore, the rate of change of the linear function is -1/3.
Thus, the initial value is 3 and the rate of change is -1/3.