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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

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MissPhiladelphia

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)

Answer:

Rate of change = -7

Initial value = 27

Step-by-step 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  

\(m=\dfrac{y_2-y_1}{x_2-x_1}\)

\(m=\dfrac{-8-27}{5-0}\)

\(m=\dfrac{-35}{5}\)

\(m=-7\)

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.

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