Answer:
[tex]f(x)=3x-3[/tex]
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
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex] ---A
[tex](x_1,y_1)=(-2,-9)[/tex]
[tex](x_2,y_2)=(0,-3)[/tex]
Substitute values in A
[tex]m = \frac{-3-(-9)}{0-(-2)}[/tex]
[tex]m = \frac{-3+9}{2}[/tex]
[tex]m = \frac{6}{2}[/tex]
[tex]m = 3[/tex]
[tex](x_1,y_1)=(1,0)[/tex]
[tex](x_2,y_2)=(3,6)[/tex]
Substitute values in A
[tex]m = \frac{6-0}{3-1}[/tex]
[tex]m = \frac{6}{2}[/tex]
[tex]m = 3[/tex]
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.
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex] ---B
[tex](x_1,y_1)=(-2,-9)[/tex]
[tex](x_2,y_2)=(0,-3)[/tex]
Substitute values in B
[tex]y+9= \frac{-3-(-9)}{0-(-2)}(x+2)[/tex]
[tex]y+9= \frac{6}{2}(x+2)[/tex]
[tex]y+9=3(x+2)[/tex]
[tex]y+9=3x+6[/tex]
[tex]y=3x+6-9[/tex]
[tex]y=3x-3[/tex]
So, [tex]f(x)=y=3x-3[/tex]
Thus Option B is true .
Hence the required equation is [tex]f(x)=3x-3[/tex]
