1. The problem is to convert the equation $y - x + 2 = 0$ into slope-intercept form. 2. The slope-intercept form of a line is given by the formula: $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. Start with the given equation: $$y - x + 2 = 0$$ 4. To isolate $y$, add $x$ and subtract $2$ from both sides: $$y = x - 2$$ 5. This is now in slope-intercept form, where the slope $m = 1$ and the y-intercept $b = -2$. 6. Therefore, the slope-intercept form of the equation is: $$y = x - 2$$