Write a equation of the line passing through the point (1,-9) that is parallel to the line Y=-3x+7

To find the equation of a line passing through the point \( (1, -9) \) that is parallel to the line \( y = -3x + 7 \), follow these steps:

### Step 1: Identify the slope of the given line
The given line is \( y = -3x + 7 \). This equation is in the slope-intercept form \( y = mx + c \), where \( m \) is the slope.

Here, the slope \( m \) of the given line is \( -3 \).

### Step 2: Use the point-slope form of the equation
The equation of a line parallel to the given line will have the same slope \( -3 \). The point-slope form of the equation of a line is:

\[
y - y_1 = m(x - x_1)
\]

where \( (x_1, y_1) \) is the point the line passes through, and \( m \) is the slope.

Substitute \( m = -3 \), \( x_1 = 1 \), and \( y_1 = -9 \):

\[
y - (-9) = -3(x - 1)
\]

Simplify the equation:

\[
y + 9 = -3x + 3
\]

### Step 3: Write the equation in slope-intercept form
Subtract 9 from both sides to solve for \( y \):

\[
y = -3x + 3 - 9
\]
\[
y = -3x - 6
\]

So, the equation of the line passing through the point \( (1, -9) \) that is parallel to the line \( y = -3x + 7 \) is:

\[
\boxed{y = -3x - 6}
\]

Would you like more details or have any questions? Here are five related questions:

1. How do you find the equation of a line perpendicular to \( y = -3x + 7 \) passing through \( (1, -9) \)?
2. What is the distance between the line \( y = -3x - 6 \) and the origin?
3. How do you find the point of intersection between the lines \( y = -3x - 6 \) and \( y = -3x + 7 \)?
4. What would be the equation of a line with the same slope but passing through the origin?
5. How does the y-intercept of a line affect its position on the graph?

**Tip:** When dealing with parallel lines, remember that their slopes are always equal. This is a key concept in identifying or constructing parallel lines in coordinate geometry.

Learn how to find the equation of a line parallel to y = -3x + 7 passing through the point (1, -9). This problem involves coordinate geometry and equations of parallel lines. Suitable for students in Grades 9-12.

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