Question

Determine the initial value and the rate of change of the linear function as given in the graph.
(-3,2.5) and (0,1)

Answer 1

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

First, let's use the two points (-3, 2.5) and (0, 1) to find the rate of change:
Rate of change (m) = (change in y) / (change in x)
m = (1 - 2.5) / (0 - (-3))
m = (1 - 2.5) / (0 + 3)
m = -1.5 / 3
m = -0.5

The rate of change of the linear function is -0.5.

To find the initial value, we can use the y-intercept. From the given points, we know that when x = 0, y = 1. This corresponds to the point (0, 1) on the graph, which means that the linear function intersects the y-axis at y = 1.

The initial value (b) of the linear function is 1.

Therefore, the linear function can be written as y = -0.5x + 1.