$$ \begin{array}{ll}\square ext { 2. Given the equation of the line, choose the slope of a perpendicular line: } \ \begin{array}{ll} ext { 1. } y=-\frac{1}{2} x-1 & ext { a. }-\frac{1}{2} \ ext { 2. } y=2 x+3 & ext { b. } \frac{1}{2} \ ext { 3. } y=\frac{1}{2} x+4 & ext { c. }-2\end{array} \ ext { 4. } y=-2 x-1 & ext { d. } 2\end{array} $$

Question

$$ \begin{array}{ll}\square 	ext { 2. Given the equation of the line, choose the slope of a perpendicular line: } \ \begin{array}{ll}	ext { 1. } y=-\frac{1}{2} x-1 & 	ext { a. }-\frac{1}{2} \ 	ext { 2. } y=2 x+3 & 	ext { b. } \frac{1}{2} \ 	ext { 3. } y=\frac{1}{2} x+4 & 	ext { c. }-2\end{array} \ 	ext { 4. } y=-2 x-1 & 	ext { d. } 2\end{array} $$

UpStudy AI · Accepted Answer

To determine the slope of a line perpendicular to each given line, recall that the slopes of perpendicular lines are **negative reciprocals** of each other. If a line has a slope $$ m $$, then a perpendicular line will have a slope of $$ -\frac{1}{m} $$.

Let's apply this to each given equation:

1. **$$ y = -\frac{1}{2}x - 1 $$**
   - **Slope ($$ m $$)**: $$ -\frac{1}{2} $$
   - **Perpendicular Slope**: $$ -\frac{1}{(-\frac{1}{2})} = 2 $$
   - **Matching Option**: **d. 2**

2. **$$ y = 2x + 3 $$**
   - **Slope ($$ m $$)**: $$ 2 $$
   - **Perpendicular Slope**: $$ -\frac{1}{2} $$
   - **Matching Option**: **a. -$$\frac{1}{2}$$**

3. **$$ y = \frac{1}{2}x + 4 $$**
   - **Slope ($$ m $$)**: $$ \frac{1}{2} $$
   - **Perpendicular Slope**: $$ -2 $$
   - **Matching Option**: **c. -2**

4. **$$ y = -2x - 1 $$**
   - **Slope ($$ m $$)**: $$ -2 $$
   - **Perpendicular Slope**: $$ \frac{1}{2} $$
   - **Matching Option**: **b. $$\frac{1}{2}$$**

### Summary of Matches:

1. **1.** $$ y = -\frac{1}{2}x - 1 $$ → **d. 2**
2. **2.** $$ y = 2x + 3 $$ → **a. -$$\frac{1}{2}$$**
3. **3.** $$ y = \frac{1}{2}x + 4 $$ → **c. -2**
4. **4.** $$ y = -2x - 1 $$ → **b. $$\frac{1}{2}$$**
The slopes of the perpendicular lines are: 1. **1.** $$ y = -\frac{1}{2}x - 1 $$ → **d. 2** 2. **2.** $$ y = 2x + 3 $$ → **a. -$$\frac{1}{2}$$** 3. **3.** $$ y = \frac{1}{2}x + 4 $$ → **c. -2** 4. **4.** $$ y = -2x - 1 $$ → **b. $$\frac{1}{2}$$**

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