To write the equation of a line that is parallel to the given line $y = -3x + 7$ and passes through the point $(1, -9)$, follow these steps:

Step 1: Identify the slope of the given line

The equation of the line is in slope-intercept form $y = mx + c$, where $m$ is the slope. For the line $y = -3x + 7$, the slope $m$ is $-3$.

Step 2: Use the point-slope form of the equation

The point-slope form of the equation of a line is given by:

$y - y_1 = m(x - x_1)$

Where:

• $m$ is the slope of the line.
• $(x_1, y_1)$ is the point through which the line passes.

Substituting the slope $m = -3$ and the point $(1, -9)$ into the equation:

$y - (-9) = -3(x - 1)$

Step 3: Simplify the equation

Now, simplify the equation:

$y + 9 = -3x + 3$

Subtract 9 from both sides:

$y = -3x + 3 - 9$

$y = -3x - 6$

Final Equation

The equation of the line parallel to $y = -3x + 7$ and passing through the point $(1, -9)$ is:

$\boxed{y = -3x - 6}$

Would you like further explanation on any part of this solution or have any other questions?

Here are some related questions:

1. What would be the equation of the line perpendicular to $y = -3x + 7$ passing through $(1, -9)$?
2. How do you find the slope of a line given two points on the line?
3. Can you convert the equation $y = -3x - 6$ to standard form?
4. What is the y-intercept of the line $y = -3x - 6$?
5. How do you determine if two lines are parallel given their equations?

Tip: Remember, parallel lines have the same slope, so their equations will differ only in the y-intercept if they are not identical.