points are (6,1) (3,2) (0,3) (3,4)
determine the initial value and the rate of change of the linear function as given in the graph. Round the answer to three decimal places needed
To find the initial value of the linear function, we can choose any of the points given and plug them into the equation in the form y = mx + b.
Let's take the point (0,3) and calculate the initial value:
3 = m(0) + b
b = 3
So, the initial value of the linear function is b = 3.
Now, to find the rate of change (slope) of the linear function, we can calculate it using two points from the given points. Let's take the points (6,1) and (3,4) to find the rate of change:
m = (4 - 1) / (3 - 6)
m = 3 / (-3)
m = -1
So, the rate of change of the linear function is m = -1.
Therefore, the linear function can be expressed as y = -x + 3.