1. The problem is to convert the equation from standard form $3x - 2y = 6$ to slope-intercept form $y = mx + b$ and verify why the conversion is correct. 2. The standard form of a linear equation is $Ax + By = C$. To convert to slope-intercept form, solve for $y$: $$By = -Ax + C$$ $$y = \frac{-A}{B}x + \frac{C}{B}$$ 3. Applying this to the equation $3x - 2y = 6$: Subtract $3x$ from both sides: $$-2y = -3x + 6$$ Divide both sides by $-2$: $$y = \frac{-3x + 6}{-2}$$ 4. Simplify the fraction by dividing each term: $$y = \frac{-3x}{-2} + \frac{6}{-2}$$ $$y = \frac{3}{2}x - 3$$ 5. The slope-intercept form is therefore: $$y = \frac{3}{2}x - 3$$ 6. The original user solution had $y = \frac{3}{2}x + 3$, which is incorrect because the constant term should be $-3$ after division. 7. The correct slope is $m = \frac{3}{2}$ and the y-intercept is $b = -3$. 8. This conversion is correct because it follows algebraic rules: isolating $y$ and dividing by the coefficient of $y$. Hence, the correct slope-intercept form is $y = \frac{3}{2}x - 3$.