1. **State the problem:** Compare the y-intercepts and rates of change (slopes) of the line given by the equation $y = 1.2x + 0.4$ and the line passing through the points $(3,4)$ and $(8,10)$. 2. **Find the slope of the line passing through the points:** $$\text{slope} = \frac{10 - 4}{8 - 3} = \frac{6}{5} = 1.2$$ 3. **Find the y-intercept of the line passing through the points:** Use the point-slope form $y = mx + b$ with $m=1.2$ and point $(3,4)$: $$4 = 1.2 \times 3 + b$$ $$4 = 3.6 + b$$ $$b = 4 - 3.6 = 0.4$$ 4. **Compare the two lines:** - The first line has slope $1.2$ and y-intercept $0.4$. - The second line has slope $1.2$ and y-intercept $0.4$. 5. **Conclusion:** Both lines have the same rate of change and the same y-intercept. **Final answer:** C. The items have the same y-intercept and the same rate of change.