Find the rate of change and the initial value of the linear function given as a table of values.
x | y
1 | 4
-3 | 8
The rate of change is m=[ ], and the initial value is b=[ ]
.
To find the rate of change, we need to calculate the slope of the line passing through the points (1, 4) and (-3, 8).
The slope formula is given by:
m = (y2 - y1) / (x2 - x1)
Plugging in the values from the table:
m = (8 - 4) / (-3 - 1)
m = 4 / (-4)
m = -1
Therefore, the rate of change is m = -1.
To find the initial value (y-intercept), we can choose one of the points and plug in the values into the equation of a line:
y = mx + b
Using the point (1,4):
4 = -1(1) + b
4 = -1 + b
b = 5
Therefore, the initial value is b = 5.
So, the rate of change is m = -1, and the initial value is b = 5.