Question

A table contains the ordered pairs (3, 42.25) and (5, 50.75). If the relationship in the table is linear, explain how to find the initial value.

Answer 1

First you can find the rate of change to be 4.25. Then you can subtract 4.25 repeatedly until you get to an output with an input of zero. The initial value is the output when the input is zero. The initial value after subtracting 4.25 three times is 29.50.

Explanation:

sample awnser

Answer 2

The initial value is 29.5

Explanation:

we know that

The linear equation in slope intercept form is equal to

`y=mx+b`

where

m is the slope

b is the y-intercept ( also called initial value)

we have the points

(3,42.25) and (5,50.75)

Find the slope m

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

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

substitute the values

`m=(50.75-42.25)/(5-3)`

`m=(8.5)/(2)`

`m=4.25`

substitute in the equation

`y=4.25x+b`

Find the value of b

with the point (3,42.25) ( or the other given point)

substitute the value of x and the value of y in the equation and solve for b

`42.25=4.25(3)+b`

`42.25=12.75+b`

`b=42.25-12.75`

`b=29.5`

substitute

The linear equation is

`y=4.25x+29.5`

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

For x=0

`y=4.25(0)+29.5`

`y=29.5`

Therefore

The initial value is 29.5