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
Let us use the table to find m and b
∵ [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] , where [tex](x_{1},y_{1})[/tex]
and [tex](x_{2},y_{2})[/tex] are any two ordered pairs in the table
∵ [tex](x_{1},y_{1})[/tex] = (1 , 20)
∵ [tex](x_{2},y_{2})[/tex] = (3 , 10)
∴ [tex]m=\frac{10-20}{3-1}=\frac{-10}{2}=-5[/tex]
∵ 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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