The points on the graph are: (-3,4), (0,3), (3,2) and (6,1)

Question

Determine the initial value and change rate of the graph. round the answer to three decimal points if needed.

Answer 1

To determine the initial value and change rate of the graph, we can use the formula for a linear equation in the form of y = mx + b, where m represents the change rate and b represents the initial value.

First, let's find the change rate (m):

Using the formula:

m = (y₂ - y₁) / (x₂ - x₁)

Pick any two points on the graph: (3,2) and (0,3)

m = (3 - 2) / (0 - 3)
m = 1 / (-3)
m = -1/3

So the change rate (m) is -1/3.

Next, let's find the initial value (b):

We can substitute any point on the graph and the change rate (m) into the equation y = mx + b and solve for b.

Using the point (0,3):
3 = (-1/3)(0) + b
3 = b

So the initial value (b) is 3.

Therefore, the equation of the graph is y = (-1/3)x + 3. The initial value is 3, and the change rate is -1/3.