1. **State the problem:** Find the equation of the blue line passing through points (1,6) and (2,10). 2. **Formula used:** The equation of a line in slope-intercept form is $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. **Calculate the slope $m$:** $$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{10 - 6}{2 - 1} = \frac{4}{1} = 4$$ 4. **Find the y-intercept $b$:** Use point (1,6) and the slope $m=4$: $$6 = 4 \times 1 + b \implies b = 6 - 4 = 2$$ 5. **Write the equation:** $$y = 4x + 2$$ 6. **Interpretation:** The line rises 4 units vertically for every 1 unit it moves horizontally, starting at $y=2$ when $x=0$. **Final answer:** $$y = 4x + 2$$