The points on the graph are: (-3,4), (0,3), (3,2) and (6,1)
Determine the initial value and change rate of the graph. round the answer to three decimal points if needed.
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.