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.

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UpStudy AI · Accepted Answer

Sure, let's address both of your questions step by step.

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### **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:**
$$ y = \frac{1}{2}x - \frac{3}{2} $$

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### **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:**
$$ 2 $$

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If you have any more questions or need further clarification, feel free to ask!
**4) The equation of the line in slope-intercept form is $$ y = \frac{1}{2}x - \frac{3}{2} $$.** **41) The simplified form of $$ (\sqrt{2})^2 $$ is 2.**

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.

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