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To write the equation of the line that is **parallel** to the given line \( y = -2x - 1 \) and passes through the point \( (4, 3) \), we need to follow these steps:

### Step 1: Identify the slope of the given line
The given line is in slope-intercept form \( y = mx + b \), where \( m \) is the slope. From \( y = -2x - 1 \), we see that the slope \( m = -2 \).

### Step 2: Use the same slope for the parallel line
Since parallel lines have the same slope, the slope of the required line is also \( m = -2 \).

### Step 3: Use the point-slope form of the equation
The equation of a line passing through a point \( (x_1, y_1) \) with slope \( m \) is given by the point-slope formula:
\[
y - y_1 = m(x - x_1)
\]
Substitute \( m = -2 \), \( x_1 = 4 \), and \( y_1 = 3 \) into the formula:
\[
y - 3 = -2(x - 4)
\]

### Step 4: Simplify the equation
Now, simplify the equation:
\[
y - 3 = -2x + 8
\]
Add 3 to both sides:
\[
y = -2x + 8 + 3
\]
\[
y = -2x + 11
\]

### Final Answer:
The equation of the line parallel to \( y = -2x - 1 \) and passing through the point \( (4, 3) \) is:
\[
y = -2x + 11
\]

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Do you want more details or have any questions?

Here are 5 related questions to extend your understanding:
1. How do you find the equation of a line that is perpendicular to a given line?
2. What would the equation be if the line passed through a different point, say \( (1, 2) \)?
3. How do you convert a line from point-slope form to slope-intercept form?
4. What is the geometric significance of two lines being parallel?
5. How does the slope change if the lines are neither parallel nor perpendicular?

**Tip:** When writing the equation of a line, always start by identifying the slope; this is key for parallel and perpendicular line problems!

Write the equation of the line parallel to the line and passing through the point y = -2x - 1, (4, 3).

Learn how to find the equation of a line parallel to y = -2x - 1 that passes through the point (4, 3). This problem involves identifying slopes and using the point-slope formula. Suitable for Grades 8-10.

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