Question

The points on the graph are (-3,2.5), (0,1), (2,0)

Determine the initial value and the rate of change of the liner function.

Answer 1

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

We can use the given points to solve for the rate of change (m) and the initial value (b).

Using the point (-3, 2.5):
2.5 = -3m + b

Using the point (0, 1):
1 = 0m + b

Simplifying the equations, we get:
2.5 = -3m + b
1 = b

Substituting b = 1 into the first equation, we get:
2.5 = -3m + 1

Solving for m:
-3m = 2.5 - 1
-3m = 1.5
m = -1.5/3
m = -0.5

Therefore, the initial value (y-intercept) is 1, and the rate of change (slope) is -0.5.