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

To find the x- and y-intercepts of the equation \(-3x + 2y = 20\), we'll follow these steps:

### 1. Find the x-intercept:
The x-intercept occurs when \(y = 0\). Substitute \(y = 0\) into the equation and solve for \(x\):

\[
-3x + 2(0) = 20
\]

\[
-3x = 20
\]

\[
x = -\frac{20}{3}
\]

So, the x-intercept is \(x = -\frac{20}{3}\).

### 2. Find the y-intercept:
The y-intercept occurs when \(x = 0\). Substitute \(x = 0\) into the equation and solve for \(y\):

\[
-3(0) + 2y = 20
\]

\[
2y = 20
\]

\[
y = \frac{20}{2} = 10
\]

So, the y-intercept is \(y = 10\).

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

Would you like any further details or have any questions?

Here are five related questions to explore further:
1. How do you graph the line given by \(-3x + 2y = 20\) using the intercepts?
2. What is the slope of the line \(-3x + 2y = 20\)?
3. How would the intercepts change if the equation were \(3x - 2y = 20\)?
4. Can you find the intercepts if the equation were given in standard form \(Ax + By = C\)?
5. What is the significance of x- and y-intercepts in real-world problems?

**Tip:** When finding intercepts, always set the other variable to zero to simplify the equation.

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

Learn how to find the x- and y-intercepts of the linear equation -3x + 2y = 20. This step-by-step solution explores key algebraic concepts, including graphing and intercepts, making it perfect for students in Grades 8-10.

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