Question

Write a linear function rule for the data in the table.x01234y31–1–3–5A.f(x) = 2x + 3B.f(x) = –2x + 3C.f(x) = 2x – 6D.f(x) = –2x – 6

Answer 1

From the given table

Choose two-point for x and y from the table

So,

The point will be:

(0, 3) and (1, 1)

Now,

From the standard for of the linear function

`y=mx+b`

Then,

First, find the value of the slope (m) from the given point

So,

From the formula of the slope:

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

Then,

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ m=\frac{1_{}-3_{}}{1_{}-0_{}} \\ m=-2 \end{gathered}`

Now,

To find the value of b, put the value of m = -2, x = 0 and y = 3 into the standard form of the equation

`\begin{gathered} y=mx+b \\ 3=-2(0)+b \\ 3=b \end{gathered}`

Then,

Put the value of b into the standard form of the equation

`\begin{gathered} y=mx+b \\ y=-2x+3 \end{gathered}`

Hence, the correct option is B.