Question

X y
0 0
2 3
Determine the initial value and the rate of change of the linear function given.

Answer 1

To determine the initial value and rate of change of a linear function, we can use the formula for a linear function in slope-intercept form:

y = mx + b

where m is the rate of change (or slope) and b is the initial value (or y-intercept).

Using the points (0,0) and (2,3), we can determine the slope:

m = (3-0)/(2-0) = 3/2

Now that we have the slope, we can determine the initial value by plugging in one of the points into the equation. Let's use (0,0):

0 = (3/2)(0) + b
b = 0

Therefore, the initial value of the linear function is 0 and the rate of change (or slope) is 3/2.

So the linear function is: y = (3/2)x.