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Bas_tet [7]
3 years ago
8

X y

Mathematics
1 answer:
Darina [25.2K]3 years ago
8 0

Answer:

Part 1) The rate of change is \frac{17}{15}

Part 2) The initial value is 68

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

Step-by-step 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=\frac{y2-y1}{x2-x1}

substitute the values

m=\frac{85-68}{15-0}

m=\frac{17}{15}

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

therefore

The rate of change is \frac{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=\frac{17}{15}

b=68

substitute

y=\frac{17}{15}x+68

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