Question

The points on the graph are (0,0) and (2,3)
Determine the initial value and the rate of change of the liner function.

Answer 1

To determine the initial value and the rate of change of the linear function, we can use the formula for the equation of a straight line, which is y = mx + b, where m is the rate of change (the slope) and b is the initial value (the y-intercept).

Using the given points (0,0) and (2,3), we can substitute these values into the equation and solve for the slope (m) and the y-intercept (b).

For the point (0,0):
0 = 0*m + b
0 = b

So, the y-intercept (b) is 0, which means the linear function passes through the origin.

For the point (2,3):
3 = 2*m + 0
3 = 2m

Solving the equation, we find:
m = 3/2

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