Question

Ethan tired to write an equation of the linear table but made a mistake. Need help it’s due today!?!?

Answer 1

Given:

The table for a linear function.

To find:

The equation of the linear function.

Solution:

If a linear function passes through two points, then the equation of linear function is:

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

Consider any two points from the given table. Let the two points are (2,-2) and (4,0). So, the equation of linear function is

`y-(-2)=(0-(-2))/(4-2)(x-2)`

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

`y+2=x-2`

Subtracting 2 from both sides.

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

`y=x-4`

So, Ethan 's made a mistake. The sign between x and 4 must be negative but in Ethan's equation it is a positive sign, which is not correct.

Therefore, the required linear equation is
`y=x-4`.