Answer :
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]
[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]
