Write the equation of the line PARALLEL to the line  y = 4x - 9 that passes through the              point (2, -4)

To find the equation of a line parallel to the given line \( y = 4x - 9 \) that passes through the point \( (2, -4) \), we follow these steps:

### Step 1: Identify the Slope
Since the lines are parallel, they have the same slope. The slope of the given line \( y = 4x - 9 \) is \( 4 \).

### Step 2: Use the Point-Slope Form
The point-slope form of a line is given by:

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

where:
- \( m \) is the slope
- \( (x_1, y_1) \) is the point the line passes through

Using the slope \( m = 4 \) and the point \( (2, -4) \):

\[
y - (-4) = 4(x - 2)
\]

Simplify the equation:

\[
y + 4 = 4x - 8
\]

### Step 3: Simplify to Slope-Intercept Form
To put the equation into the slope-intercept form \( y = mx + b \), subtract 4 from both sides:

\[
y = 4x - 8 - 4
\]

\[
y = 4x - 12
\]

### Final Equation
The equation of the line parallel to \( y = 4x - 9 \) and passing through the point \( (2, -4) \) is:

\[
\boxed{y = 4x - 12}
\]

Would you like more details or have any questions?

### Related Questions:
1. What is the slope-intercept form of a line?
2. How do you find the equation of a line perpendicular to a given line?
3. How do you determine if two lines are parallel?
4. What is the general form of a line equation?
5. How do you convert from point-slope form to standard form?

### Tip:
When working with parallel lines, always remember that their slopes are equal!

Write the equation of the line PARALLEL to the line y = 4x - 9 that passes through the point (2, -4).

Learn how to find the equation of a line parallel to y = 4x - 9 that passes through the point (2, -4). This solution uses the slope-intercept form and point-slope form of linear equations, suitable for students in Grades 8-10.

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