1. **State the problem:** Write an equation in slope-intercept form of the line that passes through the points $(-2, 3)$ and $(2, 7)$. 2. **Recall the formula for slope:** The slope $m$ of a line passing through points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ 3. **Calculate the slope:** Substitute the given points $$m = \frac{7 - 3}{2 - (-2)} = \frac{4}{2 + 2} = \frac{4}{4} = 1$$ 4. **Use the slope-intercept form:** The equation of a line is $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 5. **Find $b$ by substituting one point:** Use point $(-2, 3)$ $$3 = 1 \times (-2) + b$$ $$3 = -2 + b$$ Add 2 to both sides: $$3 + 2 = b$$ $$b = 5$$ 6. **Write the final equation:** $$y = 1x + 5$$ or simply $$y = x + 5$$