Question

Use technology to create an appropriate model of the data.

(-2,-9), (0,-3), (1,0), (3,6), (5,12)
f(x) = – 3x - 3
f(x) = 3x - 3
f(x) = - 3x + 3
f(x) = 3x + 3

Answer 1

f(x) = 3x - 3

Explanation:

Plug into TI-83/84 calculator.

Hit STAT

Hit EDIT

X-Values go in for L1

Y-Values go in for L2

Hit STAT

Scroll over to CALC

Hit #4 for LinReg (Finds line of best fit)

Enter all the way through

A is your slope

B is your y-intercept

Answer 2

`f(x)=3x-3`

Explanation:

Data : (-2,-9), (0,-3), (1,0), (3,6), (5,12)

Using technology , Plot the points on the calculator .

(Refer the attached figure)

Or

First calculate the slope of given points

`m = (y_2-y_1)/(x_2-x_1)` ---A

`(x_1,y_1)=(-2,-9)`

`(x_2,y_2)=(0,-3)`

Substitute values in A

`m = (-3-(-9))/(0-(-2))`

`m = (-3+9)/(2)`

`m = (6)/(2)`

`m = 3`

`(x_1,y_1)=(1,0)`

`(x_2,y_2)=(3,6)`

Substitute values in A

`m = (6-0)/(3-1)`

`m = (6)/(2)`

`m = 3`

Since the slopes are same .

So, the the given data is a linear function.

Now to obtain the equation for data we will use two point slope form.

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)` ---B

`(x_1,y_1)=(-2,-9)`

`(x_2,y_2)=(0,-3)`

Substitute values in B

`y+9= (-3-(-9))/(0-(-2))(x+2)`

`y+9= (6)/(2)(x+2)`

`y+9=3(x+2)`

`y+9=3x+6`

`y=3x+6-9`

`y=3x-3`

So,
`f(x)=y=3x-3`

Thus Option B is true .

Hence the required equation is
`f(x)=3x-3`