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The problem asks to find the equation of a line that is parallel to \( y = -4x + 8 \) and passes through the point \( (1, 3) \).

### Step 1: Identify the slope of the given line
The equation \( y = -4x + 8 \) is in slope-intercept form \( y = mx + b \), where \( m \) is the slope. From the equation, we can see that the slope \( m = -4 \).

### Step 2: Slope of the parallel line
Parallel lines have the same slope, so the slope of the new line will also be \( m = -4 \).

### Step 3: Use the point-slope form of the line equation
To find the equation of a line passing through the point \( (1, 3) \) with slope \( m = -4 \), we use the point-slope form:
\[
y - y_1 = m(x - x_1)
\]
Substitute \( x_1 = 1 \), \( y_1 = 3 \), and \( m = -4 \):
\[
y - 3 = -4(x - 1)
\]

### Step 4: Simplify the equation
Distribute the slope on the right side:
\[
y - 3 = -4x + 4
\]
Add 3 to both sides to solve for \( y \):
\[
y = -4x + 7
\]

Thus, the equation of the line that is parallel to \( y = -4x + 8 \) and passes through the point \( (1, 3) \) is:
\[
y = -4x + 7
\]

Would you like any further clarifications or details?

### Related Questions:
1. What is the slope-intercept form of a line?
2. How do you find the equation of a line passing through two points?
3. What is the difference between parallel and perpendicular lines?
4. How can you convert a line equation from point-slope to slope-intercept form?
5. How do you check if two lines are parallel?

### Tip:
When working with parallel lines, always remember that they share the same slope.

Write the equation of a line that is parallel to y = -4x + 8 and passes through the point (1, 3).

Find the equation of a line that is parallel to y = -4x + 8 and passes through (1, 3). This problem involves linear equations, point-slope form, and understanding parallel lines, suitable for Grades 8-10.

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