Match each equation to an equivalent equation written in slope-intercept form.

  In order down the left side, ...

Step-by-step explanation:

To put a linear equation in slope-intercept form, you solve for y, then simplify.

x -3y = -6

Subtract x and divide by -3:

  y = 1/3x +2

__

2y -6 = x

Add 6 and divide by 2:

  y = 1/2x +3

__

-x +(1/2)y = 3

Add x and multiply by 2:

  y = 2x +6

__

2x +y = 3

Subtract 2x:

  y = -2x +3

_____

Comment on the algebra

Note that when we say add, subtract, multiply, or divide by something or other, we mean to do that to both sides of the equation. That is required by the properties of equality.

If you remember the rule: do the same thing to both sides of the equation, then algebra suddenly becomes much easier.