1. **State the problem:** Find the slope-intercept form of the line passing through the points $(-2,0)$ and $(0,2)$.\n\n2. **Formula used:** The slope-intercept form is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.\n\n3. **Calculate the slope $m$:**\n$$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 0}{0 - (-2)} = \frac{2}{2} = 1$$\n\n4. **Find the y-intercept $b$:** Use one point, for example $(0,2)$, substitute into $y = mx + b$:\n$$2 = 1 \times 0 + b \implies b = 2$$\n\n5. **Write the equation:**\n$$y = 1x + 2$$\nOr simply:\n$$y = x + 2$$\n\nThis is the slope-intercept form of the line through the given points.