Question

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

Answer 1

It's a linear function.


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

Answer 2

Option D is correct

`y =3x+6`

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)} = (y_2-y_1)/(x_2-x_1)`

Substitute the given points we have;

`m = (12-9)/(2-1) = (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`