use the graph to answer the question: (-1,-4/3), (-4,-10/3).
determine the initial value and the rate of change of the linear function 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
First, let's find the slope (rate of change) using the two points (-1,-4/3) and (-4,-10/3).
Slope = (change in y) / (change in x)
Slope = (-10/3 - (-4/3)) / (-4 - (-1))
Slope = (-10/3 + 4/3) / (-4 + 1)
Slope = (-6/3) / (-3)
Slope = -2 / -3
Slope = 2/3
Now that we have found the slope, we need to find the y-intercept (initial value) of the linear function. We can use the point (-1,-4/3) to determine this.
y = mx + b (where m is the slope and b is the y-intercept)
-4/3 = (2/3)(-1) + b
-4/3 = -2/3 + b
-4/3 + 2/3 = b
-2/3 = b
So, the initial value is -2/3 and the rate of change is 2/3. Therefore, the correct answer is:
A) the initial value is -2/3, and the rate of change is 2/3.