(-3,4) , (0,3), (3,2), (6,1)

determine the initial value and the rate of change of the linear function as given. round the answer to three decimal places if needed.
the initial value is _, and the rate of change is _.

1 answer

To determine the initial value and rate of change of the linear function, we can use the formula for the slope of a line:

slope = (y2 - y1) / (x2 - x1)

Let's choose two points to calculate the slope:

Using (-3,4) and (0,3):
slope = (3 - 4) / (0 - (-3)) = -1 / 3 = -0.333

Therefore, the rate of change is -0.333.

Next, we can choose one point (-3,4) and substitute it into the linear equation y = mx + b to solve for the initial value (y-intercept), b:

4 = -0.333(-3) + b
4 = 1 + b
b = 3

Therefore, the initial value is 3.

Therefore, the linear function is: y = -0.333x + 3.