Question

X y

0 68
15 85
30 102
45 119
60 136
Determine the function rule to the linear model:
Determine the rate of change:
Determine the initial value:​

Answer 1

Part 1) The rate of change is
`(17)/(15)`

Part 2) The initial value is 68

Part 3) The function rule to the linear model is
`y=(17)/(15)x+68`

Explanation:

we know that

The linear equation in slope intercept form is equal to

`y=mx+b`

where

m is the slope or unit rate

b is the y-intercept or initial value

step 1

Find the slope

take two points from the table

(0,68) and (15,85)

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

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

substitute the values

`m=(85-68)/(15-0)`

`m=(17)/(15)`

In a linear function , the slope is the same that the rate of change

therefore

The rate of change is
`(17)/(15)`

step 2

Find the y-intercept

we know that

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

Looking at the table

For x=0, y=68

therefore

The y-intercept is

`b=68`

The y-intercept is also called the initial value

therefore

The initial value is 68

step 3

Determine the function rule to the linear model

`y=mx+b`

we have

`m=(17)/(15)`

`b=68`

substitute

`y=(17)/(15)x+68`