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To solve the system of equations by graphing, we have the following two equations:

1. \( y = -4x - 9 \)
2. \( y = 4x - 1 \)

### Step 1: Graph the first equation \( y = -4x - 9 \)
This is a linear equation in slope-intercept form \( y = mx + b \), where \( m = -4 \) (the slope) and \( b = -9 \) (the y-intercept).

- The y-intercept is \( (0, -9) \).
- Using the slope \( -4 \), we can find another point. The slope means that for every 1 unit we move to the right (along the x-axis), we move 4 units down (along the y-axis).

### Step 2: Graph the second equation \( y = 4x - 1 \)
This equation is also in slope-intercept form \( y = mx + b \), where \( m = 4 \) (the slope) and \( b = -1 \) (the y-intercept).

- The y-intercept is \( (0, -1) \).
- Using the slope \( 4 \), we can find another point. The slope means that for every 1 unit we move to the right (along the x-axis), we move 4 units up (along the y-axis).

### Step 3: Find the point of intersection
By graphing both lines, we can see where they intersect. To find the exact intersection algebraically, set the two equations equal to each other:

\[
-4x - 9 = 4x - 1
\]

Solve for \( x \):

\[
-4x - 9 = 4x - 1
\]
\[
-4x - 4x = -1 + 9
\]
\[
-8x = 8
\]
\[
x = -1
\]

Now, substitute \( x = -1 \) back into either equation to find \( y \). Using the second equation:

\[
y = 4(-1) - 1 = -4 - 1 = -5
\]

Thus, the solution is \( (x, y) = (-1, -5) \).

### Final Answer:
The solution to the system of equations is \( (-1, -5) \).

Would you like more details, or do you have any questions about this process?

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Here are 5 related questions to expand your understanding:
1. How do you interpret the slope of a line when graphing?
2. What are other methods to solve a system of equations besides graphing?
3. How can you determine if a system of equations has no solution or infinitely many solutions?
4. What does it mean if two lines are parallel when solving a system of equations by graphing?
5. Can you describe how to verify your solution by substitution?

**Tip:** Always check the slope and intercept carefully to ensure your graph is accurate!

Solve the system of equations by graphing: y = -4x - 9 and y = 4x - 1.

Learn how to solve the system of equations y = -4x - 9 and y = 4x - 1 by graphing. Understand the key concepts of graphing linear equations and identifying their point of intersection. Suitable for students in Grades 8-10.

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