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
the initial value is ____, and the rate of change is _____
To find the initial value, we can use one of the given points (either (-1,-4/3) or (-4,-10/3)). Let's use (-1,-4/3):
y = mx + b
-4/3 = m(-1) + b
-4/3 = -m + b
b = -4/3 + m
Next, let's use the other given point (-4,-10/3) to solve for m:
-10/3 = m(-4) + b
-10/3 = -4m + b
-10/3 = -4m - 4/3 + m
-10/3 = -3m - 4/3
-6 = -3m
m = 2
Now we can substitute the value of m into the initial value equation to find b:
b = -4/3 + 2
b = 2/3
Therefore, the initial value is 2/3, and the rate of change is 2.