use the image to answer the question.
the image is a line going from (-5,-4) to (5,2.8) with 2 plotted points that are (-1,-4/3) and (-4,-10/3)
determine the initial value and the rate of change of the linear function as given in the graph
A: the initial value is 2/3 and the rate of change is -2/3
B: The initial value is -2 and the rate of change is 2/3
C: the initial value is -2/3 and the rate of change is 2/3
D: the initial value is 1/6 and the rate of change is 3/2
To determine the initial value and the rate of change of the linear function, we need to use the equation of a line, which is given by y = mx + b, where m is the rate of change (slope) and b is the initial value (y-intercept).
First, let's find the rate of change (m). We can calculate the slope by using the formula:
m = (y2 - y1) / (x2 - x1)
Using the coordinates (-1, -4/3) and (-4, -10/3):
m = (-10/3 - (-4/3)) / (-4 - (-1))
m = (-10/3 + 4/3) / (-4 + 1)
m = (-6/3) / (-3)
m = -2/3
The rate of change is -2/3.
Now let's find the initial value (b). We can choose any point on the line (let's use (-1, -4/3)) and substitute the values into the equation y = mx + b to solve for b.
-4/3 = (-2/3)(-1) + b
-4/3 = 2/3 + b
-4/3 - 2/3 = b
-6/3 = b
b = -2
The initial value is -2.
Therefore, the correct answer is B: The initial value is -2 and the rate of change is 2/3.