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 values
2 | 22
8 | 25
determine the rate of change and the initial value of the linear function given here as a table values
Answers
GPT 3.5
To determine the rate of change, we need to find the difference in the y-values divided by the difference in the x-values:
Rate of change = (25 - 22) / (8 - 2)
Rate of change = 3 / 6
Rate of change = 0.5
So, the rate of change of the linear function is 0.5.
Next, we can use the rate of change to find the initial value of the linear function. We can pick one of the points given in the table to substitute into the equation of a linear function, y = mx + b, where m is the slope (rate of change) and b is the initial value. Let's use the first point (2, 22):
22 = 0.5 * 2 + b
22 = 1 + b
b = 22 - 1
b = 21
Therefore, the initial value of the linear function is 21. So, the linear function can be expressed as y = 0.5x + 21.
Rate of change = (25 - 22) / (8 - 2)
Rate of change = 3 / 6
Rate of change = 0.5
So, the rate of change of the linear function is 0.5.
Next, we can use the rate of change to find the initial value of the linear function. We can pick one of the points given in the table to substitute into the equation of a linear function, y = mx + b, where m is the slope (rate of change) and b is the initial value. Let's use the first point (2, 22):
22 = 0.5 * 2 + b
22 = 1 + b
b = 22 - 1
b = 21
Therefore, the initial value of the linear function is 21. So, the linear function can be expressed as y = 0.5x + 21.