4)) \( \frac{5}{2} \), A line has a slope of \( \frac{1}{2} \) and a \( y \)-intercept of \( -\frac{3}{2} \), Write its equation in slope-intercept form. 41) \( \sqrt{2} \hat{2} \), Write your answer using integers, proper fractions, and improper fractions in simplest form.

Sure, let's address both of your questions step by step. --- ### **4) Writing the Equation of a Line in Slope-Intercept Form** **Given:** - **Slope (m):** \( \frac{1}{2} \) - **Y-intercept (b):** \( -\frac{3}{2} \) **Slope-Intercept Form:** The slope-intercept form of a linear equation is: \[ y = mx + b \] **Plugging in the Given Values:** \[ y = \frac{1}{2}x - \frac{3}{2} \] **Final Equation:** \[ y = \frac{1}{2}x - \frac{3}{2} \] --- ### **41) Simplifying \( (\sqrt{2})^2 \)** **Expression:** \[ (\sqrt{2})^2 \] **Simplification Steps:** 1. **Understanding the Expression:** - The square of the square root of a number returns the original number. 2. **Applying the Property:** \[ (\sqrt{a})^2 = a \] 3. **Applying to Your Expression:** \[ (\sqrt{2})^2 = 2 \] **Final Answer:** \[ 2 \] --- If you have any more questions or need further clarification, feel free to ask!