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!