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.
The rate of change is M=
And the initial value is B=
First, we need to determine the slope (rate of change) of the linear function. We can use the formula:
M = (y2 - y1) / (x2 - x1)
M = (8 – 4)/ (-3 – 1)
M = 4 / -4
M = -1
Therefore, the rate of change of the linear function is -1.
Next, we need to determine the y-intercept (initial value) of the linear function. We can do this by using one of the coordinate points and the slope (rate of change) we just found. We’ll use the first point (1, 4):
y = mx + b
4 = (-1) (1) + b
4 = -1 + b
b = 5
Therefore, the initial value of the linear function is 5.
So the function in slope-intercept form is: y = -x + 5.