To determine the rate of change and the initial value of the linear function, we can use the formula for a linear function:
y = mx + b
where m is the rate of change (or the slope) and b is the initial value (or the y-intercept).
Looking at the given table, we can see that the y-values change by 3 units when the x-values increase by 6 units. Therefore, the rate of change (m) is 3/6 = 1/2.
To find the initial value (b), we can use one of the points from the table. Let's use the first point (2, 22). Plugging it into the equation, we get:
22 = (1/2)(2) + b
Simplifying, we find:
22 = 1 + b
Subtracting 1 from both sides, we get:
b = 22 - 1 = 21
Therefore, the rate of change (m) of the linear function is 1/2 and the initial value (b) is 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