A relation is plotted as a linear function on a coordinate plane starting at point C at (3, –2) and ending at point D at (–2, 3). What is the rate of change for the linear function and what is its initial value?The rate of change is and the initial value is .

Given:

A linear function starting at point C at (3, –2) and ending at point D at (–2, 3).

To find:

The rate of change and the initial value.

Solution:

If a linear function passes through two points , then the equation of linear function is

The given linear function passes through (3,-2) and (-2,3). So, the equation is

Subtracting 2 on both sides, we get

On comparing this equation with slope intercept form , where, m is slope and b is y-intercept, we get

and

Therefore, the rate of change is -1 and the initial value is 1.