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

x y
1 10
2 8
3 6
4 4
Initial value: 12, rate of change: −2
Initial value: 8, rate of change: 2
Initial value: 12, rate of change: 2
Initial value 8, rate of change: −2

1 Answer

3 votes

Answer:

Initial value
12, rate of change:
-2

Step-by-step explanation:

Step 1

Find the rate of change

we know that

In a linear equation the rate of change is equal to the slope

The formula to calculate the slope between two points is equal to


m=(y2-y1)/(x2-x1)

we have


A(1,10)\ B(2,8)

Substitute the values


m=(8-10)/(2-1)


m=-2 ----> rate of change

Step 2

Find the initial value

The equation of the line into slope-point form is equal to


y-y1=m(x-x1)

Substitute


y-10=-2(x-1)


y=-2x+2+10
y=-2x+12

The initial value is the value of y when the value of x is equal to zero (is the y-intercept)


y=-2*0+12=12----> initial value

User Selvam
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