Answer :

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]

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