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:

$m=\frac{y_2-y_1}{x_2-x_1}$

Then,

$\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{1_{}-3_{}}{1_{}-0_{}} \\ m=-2 \end{gathered}$

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.