To determine the rate of change and the initial value of the linear function given in the table, we need to calculate the slope (rate of change) and the y-intercept (initial value).
Rate of change (slope):
The rate of change (slope) of a linear function can be calculated using the formula:
slope = (change in y) / (change in x)
From the table, we can calculate the change in y and the change in x as follows:
change in y = 25 - 22 = 3
change in x = 8 - 2 = 6
Now, we can calculate the slope:
slope = 3 / 6 = 0.5
Initial value (y-intercept):
To find the initial value (y-intercept), we can use the equation of a line in the form y = mx + b, where m is the slope and b is the y-intercept.
From the table, we can see that when x = 2, y = 22. We can plug these values into the equation and solve for the y-intercept:
22 = 0.5 * 2 + b
22 = 1 + b
b = 22 - 1
b = 21
Therefore, the rate of change (slope) of the linear function is 0.5 and the initial value (y-intercept) is 21. The linear function can be expressed as y = 0.5x + 21.
Use the table to answer the question.
x y
2 22
8 25
Determine the rate of change and the initial value of the linear function given here as a table of values
1 answer