To solve the problem of finding the equation of a line parallel to $y = -3x - 5$ that passes through the point (-2, 4), we can follow these steps:

Step 1: Identify the slope of the given line

The slope of the line given by $y = -3x - 5$ is $-3$, since the equation is in slope-intercept form $y = mx + b$, where $m$ is the slope.

Since the new line is parallel to this line, it will have the same slope. Thus, the slope of the new line is also $-3$.

Step 2: Use the point-slope form

The equation of a line in point-slope form is given by: $y - y_1 = m(x - x_1)$ where $m$ is the slope and $(x_1, y_1)$ is a point on the line.

In this case:

• $m = -3$
• $(x_1, y_1) = (-2, 4)$

Substitute these values into the point-slope form: $y - 4 = -3(x - (-2))$ Simplify: $y - 4 = -3(x + 2)$

Step 3: Solve for the unknown number

In the image, the equation is written as: $y - ? = -3(x + 2)$ Comparing this with our equation $y - 4 = -3(x + 2)$, it is clear that the number in the "?" position should be 4.

Thus, the correct number is 4.

Would you like more details on any of the steps?

Here are 5 questions related to this problem:

1. How do we know that two lines are parallel by looking at their equations?
2. What happens if two lines have the same slope but different y-intercepts?
3. Can we use other forms of a line’s equation to find the same result?
4. What if the problem asked for a line perpendicular to $y = -3x - 5$?
5. How would the equation change if the point were different?

Tip: Always check that your equation matches the given condition (in this case, being parallel and passing through the specific point).