Question

Use technology to create an appropriate model of the data.

Answer 1

Answer:

f(x) = 3x - 3

Step-by-step 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

Answer:

$f(x)=3x-3$  

Step-by-step 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

$m = \frac{y_2-y_1}{x_2-x_1}$   ---A

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

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

Substitute values in A

$m = \frac{-3-(-9)}{0-(-2)}$

$m = \frac{-3+9}{2}$

$m = \frac{6}{2}$

$m = 3$

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

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

Substitute values in A

$m = \frac{6-0}{3-1}$

$m = \frac{6}{2}$

$m = 3$

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.

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$   ---B

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

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

Substitute values in B

$y+9= \frac{-3-(-9)}{0-(-2)}(x+2)$  

$y+9= \frac{6}{2}(x+2)$  

$y+9=3(x+2)$  

$y+9=3x+6$  

$y=3x+6-9$  

$y=3x-3$  

So, $f(x)=y=3x-3$  

Thus Option B is true .

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