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
2 22
8 25
determine the rate of change and the initial value of the linear function given here as a table of values
Answers
GPT 3.5
To determine the rate of change and the initial value of the linear function, we need to find the slope of the function. The slope (rate of change) is calculated by taking the difference in the y-values divided by the difference in the x-values.
In this case, the difference in y-values is 25-22 = 3 and the difference in x-values is 8-2 = 6.
Therefore, the slope (rate of change) of the linear function is 3/6 = 0.5.
Next, we can use the slope-intercept form of a linear function, y = mx + b, where m is the slope and b is the y-intercept.
From the table of values, we can use the point (2, 22) to find the initial value (y-intercept).
22 = 0.5(2) + b
22 = 1 + b
b = 21
So, the initial value of the linear function is 21.
Therefore, the linear function can be written as:
y = 0.5x + 21
In this case, the difference in y-values is 25-22 = 3 and the difference in x-values is 8-2 = 6.
Therefore, the slope (rate of change) of the linear function is 3/6 = 0.5.
Next, we can use the slope-intercept form of a linear function, y = mx + b, where m is the slope and b is the y-intercept.
From the table of values, we can use the point (2, 22) to find the initial value (y-intercept).
22 = 0.5(2) + b
22 = 1 + b
b = 21
So, the initial value of the linear function is 21.
Therefore, the linear function can be written as:
y = 0.5x + 21