Answered

Find the best answers to your questions at Westonci.ca, where experts and enthusiasts provide accurate, reliable information. Get quick and reliable solutions to your questions from a community of experienced professionals on our platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

Which function rule represents the data table below:
Input(x)1,2,3,4,5
Output(y)9,12,15,18,21
A~y=4+5x
B~y=3+6x
C~y=5+4x
D~y=6+3x
I think B

Sagot :

naǫ
It's a linear function.

[tex]x_1=1 \\ y_1=9 \\ \\ x_2=2 \\ y_2=12 \\ \\ m=\frac{y_2-y_1}{x_2-x_1}=\frac{12-9}{2-1}=\frac{3}{1}=3 \\ \\ y=3x+b \\ (1,9) \\ 9=3 \times 1+b \\ 9=3+b \\ 9-3=b \\ b=6 \\ \\ y=3x+6 \\ \boxed{y=6+3x} \Leftarrow \hbox{answer D}[/tex]

Answer:

Option D is correct

[tex]y =3x+6[/tex]

Step-by-step explanation:

Using slope-intercept form:

The equation of line is given by:

[tex]y = mx+b[/tex]          .....[1]

where, m is the slope of the line and b is the y-intercept.

From the given table

Consider coordinates in the form of (x, y)

i,e (1, 9) and (2, 12)

Calculate slope:

[tex]\text{Slope (m)} = \frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the given points we have;

[tex]m = \frac{12-9}{2-1} = \frac{3}{1} = 3[/tex]

Substitute this in [1] we have;

[tex]y =3x+b[/tex]

Substitute any point from the given table to find b:

Substitute (4, 18) we get;

[tex]18 = 4(3) +b[/tex]

18 = 12+b

Subtract 12 from both sides we have;

6 = b

or

b = 2

⇒[tex]y =3x+6[/tex] or y = 6+3x

therefore,  function rule represents the  given data table is, [tex]y =3x+6[/tex]

We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We hope this was helpful. Please come back whenever you need more information or answers to your queries. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.