Find the x- and y-intercepts of the graph of minus, 3, x, plus, 2, y, equals, 20−3x+2y=20. State each answer as an integer or an improper fraction in simplest form.

You are asked to find the **x-intercept** and **y-intercept** of the equation \( -3x + 2y = 20 \).

### **Finding the x-intercept:**

The **x-intercept** occurs when \( y = 0 \). Substitute \( y = 0 \) into the equation and solve for \( x \):
\[
-3x + 2(0) = 20
\]
\[
-3x = 20
\]
\[
x = -\frac{20}{3}
\]
Thus, the **x-intercept** is \( \left( -\frac{20}{3}, 0 \right) \).

### **Finding the y-intercept:**

The **y-intercept** occurs when \( x = 0 \). Substitute \( x = 0 \) into the equation and solve for \( y \):
\[
-3(0) + 2y = 20
\]
\[
2y = 20
\]
\[
y = 10
\]
Thus, the **y-intercept** is \( (0, 10) \).

### Final Answer:
- The **x-intercept** is \( \left( -\frac{20}{3}, 0 \right) \).
- The **y-intercept** is \( (0, 10) \).

Would you like further details or have any questions?

Here are 8 related questions:
1. How do you find intercepts for any linear equation?
2. How would the intercepts change if the equation were \( 3x - 2y = 20 \)?
3. Can a linear equation have more than one x-intercept or y-intercept?
4. What do intercepts represent on a graph?
5. How would you graph the equation \( -3x + 2y = 20 \) using the intercepts?
6. What is the slope of the line \( -3x + 2y = 20 \)?
7. How do you convert the equation \( -3x + 2y = 20 \) into slope-intercept form?
8. How do intercepts help in quickly sketching the graph of a linear equation?

**Tip:** For linear equations, finding intercepts provides key points that help in graphing the line efficiently.

Learn how to find the x and y intercepts of the linear equation -3x + 2y = 20 using step-by-step solutions. Understand the concepts of intercepts and their significance in graphing linear equations. Suitable for Grades 7-9 students.

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