Question

Determine the initial value and the racte of change of the linear function as given in the graph. Round the answer to three decimal places as needed. (1 point)
(-3,4) (0,3) (3,2) (6,1)

Answer 1

what is the rate of change

Answer 2

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.

Answer 3

The rate of change of the linear function is -1/3.