Question

What is the function rule represented by the following table? x y 0 0 1 -2 -2 4 y = -x - 1 y = -2x y = x - 3 y = -3x + 2

Answer 1

y = -2 x - 1

Explanation:

Answer 2

`y = -2x`

Explanation:

Given

x || 0 || 1 || -2

y || 0 || -2 || 4

Required

Determine the function rule

First, we have to determine the slope of the function using;

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

Where x and y represent any two corresponding values of x and y

When x = 0; y = 0
`(x_1,y_1)`

When x = 1; y = -2
`(x_2,y_2)`

Substitute these values in
`m = (y_1 - y_2)/(x_1 - x_2)`

`m = (0 - (-2))/(0 - 1)`

`m = (0 +2)/(0 - 1)`

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

`m = -2`

Next, is to determine the function rule; using slope intercept form as follows;

`y - y_1 = m(x - x_1)`

Take any corresponding values of x and y as x1 and x2

When x = -2; y = 4

`y - y_1 = m(x - x_1)` becomes

`y - 4 = -2(x - (-2))`

`y - 4 = -2(x + 2)`

Open the bracket

`y - 4 = -2x -4`

Add 4 to both sides

`y - 4 + 4 = -2x - 4 + 4`

`y = -2x`

Hence, the function rule is
`y = -2x`