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 $y = 9x$:

plaintextCopy code
    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.