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.