Question

A relation is plotted as a linear function on the coordinate plane starting at point e (0, 27)(0, 27) and ending at point f (5,−8)(5,−8) . what is the rate of change for the linear function and what is its initial value? select from the drop-down menus to correctly complete the statements. the rate of change for the linear function is

Answer 1

Rate of change = -7

Initial value = 27

Explanation:

It is given that a linear function starting at point e(0, 27) and ending at point f(5,−8).

We need to find the rate of change for the linear function and its initial value.

If a linear function passes through two points then the rate of change is

`m=(y_2-y_1)/(x_2-x_1)`

`m=(-8-27)/(5-0)`

`m=(-35)/(5)`

`m=-7`

The rate of change for the linear function is -7.

The initial value of a function is its y-intercept, where x=0.

From the given points it is clear that the value of function is 27 at x=0.

Therefore, the initial value is 27.

Answer 2

The rate of change of a linear function is equal to the slope of the function, Slope, m = ( y1 – y2) / (x1 – x2)
M = ( 27 – ( -8)) / ( 0 – 5)
M = -7
At ( 0, 27)
27 = 0(-7) + b
B = 27 So the initial value ( 0, 27)