Question
x | y
2 | 22
8 | 23
determine the rate of change and the initial value of the linear function given here as a table values
2 | 22
8 | 23
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 and the initial value of the linear function represented by the given values, we can use the formula for the slope of a line:
Slope (m) = (y2 - y1) / (x2 - x1)
Let's use the two points provided (2, 22) and (8, 23):
m = (23 - 22) / (8 - 2)
m = 1 / 6
m = 1/6
So, the rate of change (slope) of the linear function is 1/6.
Next, we can find the initial value by substituting one of the points and the slope into the equation of a straight line, y = mx + b, and solving for b:
Using the point (2, 22) and the slope 1/6:
22 = (1/6) * 2 + b
22 = 1/3 + b
b = 22 - 1/3
b = 66/3 - 1/3
b = 65/3
Therefore, the initial value (y-intercept) of the linear function is 65/3.
Slope (m) = (y2 - y1) / (x2 - x1)
Let's use the two points provided (2, 22) and (8, 23):
m = (23 - 22) / (8 - 2)
m = 1 / 6
m = 1/6
So, the rate of change (slope) of the linear function is 1/6.
Next, we can find the initial value by substituting one of the points and the slope into the equation of a straight line, y = mx + b, and solving for b:
Using the point (2, 22) and the slope 1/6:
22 = (1/6) * 2 + b
22 = 1/3 + b
b = 22 - 1/3
b = 66/3 - 1/3
b = 65/3
Therefore, the initial value (y-intercept) of the linear function is 65/3.