Change equation into y=mx+b

2(x-3)+3y=0

y = -⅔x + 2

Step-by-step explanation:

Given the linear equation, 2(x-3) + 3y = 0, for which we must transform into its slope-intercept form, y = mx + b:

First, distribute 2 into the parenthesis:

2(x-3) + 3y = 0

2x - 6 + 3y = 0

Next, subtract both sides by 2x:

2x - 2x - 6 + 3y = - 2x

Then, add 6 to both sides of the equation:

- 6 + 6 + 3y = - 2x + 6

3y = -2x + 6

Lastly, divide both sides by 3 to isolate y:

y = - ⅔x + 2 ⇒ This is the slope-intercept form.

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