To solve the problem in your uploaded image, let’s analyze the given question:

We are tasked to find the equation of a line that is parallel to $y = -2x - 7$ and passes through the point $(9, -1)$.

Key Steps to Solve:

1. Understand parallel lines:

   • Parallel lines have the same slope.
   • The slope of the given line $y = -2x - 7$ is $m = -2$.

2. Use the point-slope form of a line: $y - y_1 = m(x - x_1)$ Substitute $m = -2$, $x_1 = 9$, and $y_1 = -1$.

   $y - (-1) = -2(x - 9)$

3. Simplify the equation: $y + 1 = -2(x - 9)$ Distribute: $y + 1 = -2x + 18$ Subtract 1 from both sides: $y = -2x + 17$

Final Equation:

The equation of the line is $y = -2x + 17$.

Correct Answer from Choices:

The correct choice is: $\boxed{y = -2x + 17}$

Would you like further explanation on why we use the point-slope form or another part of this problem? Let me know! 😊

Here are some follow-up questions to expand your understanding:

1. What is the difference between parallel and perpendicular lines in terms of slope?
2. How do you find the equation of a line perpendicular to $y = -2x - 7$?
3. Can you write an equation if given two points instead of a point and a slope?
4. Why does changing the y-intercept not affect the slope of a line?
5. How can you verify that two lines are parallel using their equations?

Tip: Always double-check whether the line should be parallel or perpendicular—this can change your approach entirely!