through: $$ (-1,0) $$, perp. to $$ y=-x-4 $$

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UpStudy AI · Accepted Answer

To find the equation of the line that is **perpendicular** to $$ y = -x - 4 $$ and **passes through** the point $$ (-1, 0) $$, 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**,
- $$ b $$ is the **y-intercept**.

For $$ y = -x - 4 $$:
$$
m_1 = -1
$$

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

Lines that are perpendicular to each other have slopes that are **negative reciprocals**.

$$
m_2 = -\frac{1}{m_1} = -\frac{1}{-1} = 1
$$

So, the slope of the perpendicular line is $$ m_2 = 1 $$.

### 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:
- $$ (x_1, y_1) $$ is a point on the line,
- $$ m $$ is the slope.

Given the point $$ (-1, 0) $$ and slope $$ m_2 = 1 $$:
$$
y - 0 = 1(x - (-1))
$$
$$
y = 1(x + 1)
$$
$$
y = x + 1
$$

### **Final Answer**

The equation of the line **perpendicular** to $$ y = -x - 4 $$ and **passing through** the point $$ (-1, 0) $$ is:
$$
\boxed{y = x + 1}
$$
The equation of the line perpendicular to $$ y = -x - 4 $$ and passing through $$ (-1, 0) $$ is $$ y = x + 1 $$.

through: , perp. to

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