Question

(-3, 2.5), (0,1), (2,0) Determine the initial value and the rate of change of the linear function as given in the graph. The initial value is , and the rate of change is.

Answer 1

To determine the initial value and the rate of change of the linear function, we need to find the equation of the line that passes through the given points.

First, let's find the slope (rate of change) of the line using the formula:
m = (y2 - y1) / (x2 - x1)

Using the points (-3, 2.5) and (0, 1):
m = (1 - 2.5) / (0 - (-3))
m = -1.5 / 3
m = -0.5

Now, let's use the point-slope form of a linear equation to find the equation of the line:
y - y1 = m(x - x1)

Using the point (0, 1):
y - 1 = -0.5(x - 0)
y - 1 = -0.5x

To find the initial value, we can set x = 0 and solve for y:
y - 1 = -0.5(0)
y - 1 = 0
y = 1

Therefore, the initial value is 1 and the rate of change is -0.5.