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=
.
To find the rate of change and the initial value of the linear function from a table of values, we need to calculate the slope and the y-intercept.
Let's say we have a table of values for a linear function:
x | y
1 | 3
2 | 5
To calculate the rate of change (m) or slope, we use the formula:
m = (y2 - y1) / (x2 - x1)
Using the values from the table:
m = (5 - 3) / (2 - 1)
m = 2 / 1
m = 2
So, the rate of change or slope is m = 2.
To calculate the initial value (b) or y-intercept, we can use the slope-intercept form of a linear equation: y = mx + b. We can substitute one of the points in the table into this equation to solve for b.
Using the point (1, 3):
3 = 2(1) + b
3 = 2 + b
b = 3 - 2
b = 1
So, the initial value or y-intercept is b = 1.
Therefore, the rate of change is m = 2, and the initial value is b = 1.