Question

Determine the rate of change and the initial value of the linear function given here as a table of values x 2,4 y22,25

Answer 1

To determine the rate of change and the initial value of the linear function given the table of values x and y, we first need to find the slope of the line. The slope of a linear function can be computed using the formula:

slope (m) = (y2 - y1) / (x2 - x1)

Given the values from the table:

x1 = 2, y1 = 22
x2 = 4, y2 = 25

slope (m) = (25 - 22) / (4 - 2) = 3 / 2 = 1.5

Therefore, the rate of change (slope) of the linear function is 1.5.

Next, we can use one of the points to determine the initial value (y-intercept) of the linear function. Let's use the point (2, 22):

y = mx + b

Substitute the values of m, x, and y into the equation:

22 = 1.5 * 2 + b
22 = 3 + b
b = 19

Therefore, the initial value (y-intercept) of the linear function is 19.

So, the linear function can be represented as:

y = 1.5x + 19