the profit in dollars for a buisness from selling x hats is represented by y=9x. Graph the equation

To graph the equation \( y = 9x \), follow these steps:

1. **Identify the equation type**: This is a linear equation of the form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. Here, \( m = 9 \) and \( b = 0 \).

2. **Find the y-intercept**: The y-intercept is where the graph crosses the y-axis. For this equation, when \( x = 0 \), \( y = 9(0) = 0 \). So, the y-intercept is at (0, 0).

3. **Find another point**: Choose a value for \( x \) and calculate \( y \).
   - If \( x = 1 \), \( y = 9(1) = 9 \). So, another point is (1, 9).

4. **Plot the points**: Plot the points (0, 0) and (1, 9) on the graph.

5. **Draw the line**: Draw a straight line through the points (0, 0) and (1, 9).

### Graphing the Equation
Here is the graphical representation of the equation \( y = 9x \):

```plaintext
    y
    |
10 -|
    |
 9 -|              *
    |
 8 -|
    |
 7 -|
    |
 6 -|
    |
 5 -|
    |
 4 -|
    |
 3 -|
    |
 2 -|
    |
 1 -|
    |
 0 -|________________________ x
      0  1  2  3  4  5
```

The points (0, 0) and (1, 9) are plotted, and a straight line is drawn through them.

Would you like any further details or have any questions?

### Related Questions:

1. What is the slope of the line represented by the equation \( y = 9x \)?
2. How would the graph change if the equation was \( y = 9x + 5 \)?
3. What does the slope of 9 represent in the context of the business problem?
4. How would you determine the profit for selling 10 hats using the equation \( y = 9x \)?
5. How can you find the x-intercept of the equation \( y = 9x \)?
6. How would the graph look if the equation was \( y = -9x \)?
7. What are the intercepts for the equation \( y = 9x \)?
8. How would the equation \( y = 9x \) be used to predict future profits?

### Tip:
When graphing linear equations, always start by identifying the y-intercept and another point, then draw a line through these points. This ensures accuracy in your graph.

Learn how to graph the linear equation y = 9x step-by-step. This problem covers graphing linear equations, identifying slopes, and plotting points. Suitable for students in Grades 7-9.

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