1. **State the problem:** We are given two sets of measurements for Blue Ribbon and Red Ribbon lengths in inches: Blue Ribbon: 0.25, 1.25 and Red Ribbon: 6, 15. 2. **Identify the relationship:** We want to find the relationship between Blue Ribbon length ($x$) and Red Ribbon length ($y$). This can be modeled as a linear function $y = mx + b$ where $m$ is the slope and $b$ is the y-intercept. 3. **Calculate the slope $m$:** $$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{15 - 6}{1.25 - 0.25} = \frac{9}{1} = 9$$ 4. **Find the y-intercept $b$:** Use one point, for example $(0.25, 6)$: $$6 = 9 \times 0.25 + b$$ $$6 = 2.25 + b$$ $$b = 6 - 2.25 = 3.75$$ 5. **Write the equation:** $$y = 9x + 3.75$$ 6. **Interpretation:** For every inch of Blue Ribbon, the Red Ribbon length increases by 9 inches plus a base length of 3.75 inches. **Final answer:** $$y = 9x + 3.75$$