Verified Answer :

naǫ

It's a linear function.

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

Answer:

Option D is correct

\(y =3x+6\)

Step-by-step explanation:

Using slope-intercept form:

The equation of line is given by:

\(y = mx+b\)          .....[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:

\(\text{Slope (m)} = \frac{y_2-y_1}{x_2-x_1}\)

Substitute the given points we have;

\(m = \frac{12-9}{2-1} = \frac{3}{1} = 3\)

Substitute this in [1] we have;

\(y =3x+b\)

Substitute any point from the given table to find b:

Substitute (4, 18) we get;

\(18 = 4(3) +b\)

18 = 12+b

Subtract 12 from both sides we have;

6 = b

or

b = 2

⇒\(y =3x+6\) or y = 6+3x

therefore,  function rule represents the  given data table is, \(y =3x+6\)

Related Questions