Mathematics

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

2 Answer

  •  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  

    [tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

    [tex]m=\dfrac{-8-27}{5-0}[/tex]

    [tex]m=\dfrac{-35}{5}[/tex]

    [tex]m=-7[/tex]

    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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