https://file.aiquickdraw.com/mathbot/file/1727211883957c6bxzosm.jpg

Let's break down the problem from the image:

You have $30 to spend on pens and pencils. 
- Pens cost $2 per package.
- Pencils cost $1.50 per package.

We need to find and interpret both the **x-intercept** and **y-intercept**.

### Step 1: Setting Up the Equation
Let:
- $ x $ represent the number of packages of pens.
- $ y $ represent the number of packages of pencils.

The total cost of pens and pencils is given by:
\[
2x + 1.5y = 30
\]
This equation represents all possible combinations of pens and pencils that you can buy with $30.

### Step 2: Finding the Intercepts

- **x-intercept**: The x-intercept occurs when $ y = 0 $ (i.e., no pencils are bought). Substituting $ y = 0 $ into the equation:
  \[
  2x + 1.5(0) = 30
  \]
  \[
  2x = 30
  \]
  \[
  x = 15
  \]
  Interpretation: If you spend all $30 on pens, you can buy 15 packages of pens and no pencils.

- **y-intercept**: The y-intercept occurs when $ x = 0 $ (i.e., no pens are bought). Substituting $ x = 0 $ into the equation:
  \[
  2(0) + 1.5y = 30
  \]
  \[
  1.5y = 30
  \]
  \[
  y = 20
  \]
  Interpretation: If you spend all $30 on pencils, you can buy 20 packages of pencils and no pens.

### Final Answer:
- **x-intercept**: $ x = 15 $, meaning you can buy 15 packages of pens with no pencils.
- **y-intercept**: $ y = 20 $, meaning you can buy 20 packages of pencils with no pens.

Would you like to go into more details or have any questions?

Here are 5 related questions to explore:
1. What would happen if the price of pens increased to $3 per package?
2. How would the intercepts change if you only had $25 to spend?
3. Can you graph the line based on the equation $ 2x + 1.5y = 30 $?
4. What would the slope of this equation represent in real-life terms?
5. How many total combinations of pens and pencils can you buy within the $30 limit?

**Tip:** To find the intercepts of any linear equation, set one variable to zero and solve for the other!

You have $30 to spend on pens and pencils. The pens cost $2 per package and the pencils cost $1.50 per package. Find and interpret both the x and y intercepts.

Learn how to solve the linear equation 2x + 1.5y = 30 by finding the x and y intercepts. This problem covers key algebraic concepts and is ideal for students in Grades 7-9.

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