Question 14
Write an equation for a line perpendicular to and passing through the point

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Ask by Cox Carlson. in the United States

Jan 24,2025

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Question 14 Write an equation for a line perpendicular to $$ y=-2 x-2 $$ and passing through the point $$ (4,1) $$ $$ y=\square $$ Question Help:Masmit Message instructor Substion

UpStudy AI · Accepted Answer

To find the equation of a line perpendicular to $$ y = -2x - 2 $$ and passing through the point $$ (4, 1) $$, follow these steps:

### 1. **Determine the Slope of the Given Line**

The given equation is in the slope-intercept form $$ y = mx + b $$, where $$ m $$ is the slope.

$$ y = -2x - 2 $$

So, the slope ($$ m $$) of the given line is **-2**.

### 2. **Find the Slope of the Perpendicular Line**

Perpendicular lines have slopes that are negative reciprocals of each other.

$$ m_{\text{perpendicular}} = -\frac{1}{m} = -\frac{1}{-2} = \frac{1}{2} $$

So, the slope of the perpendicular line is **$$ \frac{1}{2} $$**.

### 3. **Use the Point-Slope Form to Find the Equation**

The point-slope form of a line is:

$$ y - y_1 = m(x - x_1) $$

Where:
- $$ m $$ is the slope
- $$ (x_1, y_1) $$ is the point the line passes through

Plugging in the values:

$$ y - 1 = \frac{1}{2}(x - 4) $$

### 4. **Simplify to Slope-Intercept Form**

Expand and simplify the equation:

$$
\begin{align*}
y - 1 &= \frac{1}{2}x - 2 \
y &= \frac{1}{2}x - 2 + 1 \
y &= \frac{1}{2}x - 1
\end{align*}
$$

### **Final Equation**

$$ y = \frac{1}{2}x - 1 $$

**Answer:** 
$$ y = \frac{1}{2}x - 1 $$
The equation of the line perpendicular to $$ y = -2x - 2 $$ and passing through the point $$ (4, 1) $$ is $$ y = \frac{1}{2}x - 1 $$.

Question 14
Write an equation for a line perpendicular to and passing through the point

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Question 14 Write an equation for a line perpendicular to and passing through the point Question Help:Masmit Message instructor Substion