To find the rate of change (m) of a linear function, we calculate the change in y divided by the change in x:
m = (change in y) / (change in x)
Let's calculate the change in y and change in x:
change in y = 8 - 4 = 4
change in x = -3 - 1 = -4
Now we can substitute the values into the formula to find the rate of change:
m = 4 / -4 = -1
So the rate of change is m = -1.
To find the initial value (b) of the linear function, we can choose any point from the table and substitute its values into the equation:
Let's use the first point (1, 4):
y = mx + b
4 = -1(1) + b
Solving for b:
4 = -1 + b
b = 4 + 1
b = 5
Therefore, the initial value is b = 5.
In summary, the rate of change is m = -1, and the initial value is b = 5.
x y
1 4
−3 8
Find the rate of change and the initial value of the linear function given as a table of values.
(1 point)
The rate of change is m=
, and the initial value is b=
.
1 answer