Question

Determine the initial value and the rate of change of the linear function given in the graph. the graph does through the points (0,0), and (2,3). The initial value is , and the rate of change is

Answer 1

To determine the initial value and the rate of change of the linear function given in the graph, we can use the formula for a linear function: y = mx + b

Given that the graph goes through the points (0,0) and (2,3), we can substitute these values into the equation to form two equations:

0 = m(0) + b ... (equation 1)
3 = m(2) + b ... (equation 2)

From equation 1, we can see that the initial value (b) is 0 since when x = 0, y is also 0.

From equation 2, we can solve for the rate of change (m):

3 = 2m + 0
2m = 3
m = 3/2

Therefore, the initial value is 0, and the rate of change is 3/2.