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=
use slope y-intercept form
To find the rate of change (slope), we can use the formula:
M = (y2 - y1) / (x2 - x1)
Taking the first two points from the table, we get:
M = (8 - 4) / (-3 - 1) = -4 / 4 = -1
So the rate of change is -1.
To find the initial value (y-intercept), we can use the slope-intercept form of a linear equation:
y = mx + b
where m is the slope and b is the y-intercept. We can use one of the points from the table and the slope we just found to solve for b:
4 = -1(1) + b
b = 4 + 1 = 5
So the initial value is 5.
Therefore, the linear function given by this table of values is:
y = -x + 5