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:​

Respuesta :

Answer:

Part 1) The rate of change is [tex]\frac{17}{15}[/tex]

Part 2) The initial value is 68

Part 3) The function rule to the linear model is [tex]y=\frac{17}{15}x+68[/tex]

Step-by-step explanation:

we know that

The linear equation in slope intercept form is equal to

[tex]y=mx+b[/tex]

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

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

substitute the values

[tex]m=\frac{85-68}{15-0}[/tex]

[tex]m=\frac{17}{15}[/tex]

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

therefore

The rate of change is [tex]\frac{17}{15}[/tex]

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

[tex]b=68[/tex]

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

[tex]y=mx+b[/tex]

we have

[tex]m=\frac{17}{15}[/tex]

[tex]b=68[/tex]

substitute

[tex]y=\frac{17}{15}x+68[/tex]

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