Question

What is the rate of change and initial value for the linear relation that includes the points shown in the table?

Answer 1

The initial value: 25, rate of change: -5 ⇒ answer C

Step-by-step explanation:

The table:

→  x  :    1    :    3    :    5    :    7

→  y  :    20 :    10  :    0    :    -10

The linear relation between x and y is y = m x + b, where

• m is the rate of change
• b is the initial value

Let us use the table to find m and b

∵ $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ , where $(x_{1},y_{1})$

   and $(x_{2},y_{2})$ are any two ordered pairs in the table

∵ $(x_{1},y_{1})$ = (1 , 20)

∵ $(x_{2},y_{2})$ = (3 , 10)

∴ $m=\frac{10-20}{3-1}=\frac{-10}{2}=-5$

∵ m is the rate of change

∴ The rate of change is -5

Substitute the value of m in the form of the linear relation

∴ y = -5 x + b

To find b substitute x and y in the equation by the coordinates of any points in the table, let us chose point (5 , 0)

∵ x = 5 and y = 0

∴ 0 = -5(5) + b

∴ 0 = -25 + b

- Add 25 to both sides

∴ 25 = b

∵ b represents the initial value

∴ The initial value is 25

The initial value: 25, rate of change: -5

Learn more:

You can learn more about the linear equation in brainly.com/question/4326955

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