through: $$ (4,-2) $$, parallel to $$ y=-x+1 $$

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UpStudy AI · Accepted Answer

To find the equation of a line that **passes through the point (4, -2)** and is **parallel to the line $$ y = -x + 1 $$**, follow these steps:

1. **Determine the slope of the given line:**
   
   The equation $$ y = -x + 1 $$ is in the slope-intercept form $$ y = mx + b $$, where:
   - $$ m $$ is the slope
   - $$ b $$ is the y-intercept

For $$ y = -x + 1 $$:
   - **Slope ($$ m $$) = -1**

2. **Since parallel lines have the same slope:**
   
   The desired line will also have a slope of **-1**.

3. **Use the point-slope form to find the equation of the desired line:**
   
   The point-slope form is:
   $$
   y - y_1 = m(x - x_1)
   $$
   
   Plugging in $$ m = -1 $$ and the point $$ (4, -2) $$:
   $$
   y - (-2) = -1(x - 4)
   $$
   $$
   y + 2 = -x + 4
   $$

4. **Solve for $$ y $$ to get the slope-intercept form:**
   $$
   y = -x + 4 - 2
   $$
   $$
   y = -x + 2
   $$

**Final Answer:**
$$
y = -x + 2
$$
The equation of the line is $$ y = -x + 2 $$.

through: , parallel to

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