Let's solve for the x- and y-intercepts of the equation $3x - 2y = 10$.

Step 1: Finding the x-intercept

The x-intercept occurs when $y = 0$. To find it, substitute $y = 0$ into the equation and solve for $x$.

$3x - 2(0) = 10$

This simplifies to:

$3x = 10$

Now solve for $x$:

$x = \frac{10}{3}$

So, the x-intercept is $\left(\frac{10}{3}, 0\right)$.

Step 2: Finding the y-intercept

The y-intercept occurs when $x = 0$. To find it, substitute $x = 0$ into the equation and solve for $y$.

$3(0) - 2y = 10$

This simplifies to:

$-2y = 10$

Now solve for $y$:

$y = \frac{-10}{2} = -5$

So, the y-intercept is $(0, -5)$.

Conclusion

• x-intercept: $\left(\frac{10}{3}, 0\right)$
• y-intercept: $(0, -5)$

Would you like further explanation on the process or any other details? Here are 5 related questions to explore:

1. How would the intercepts change if the equation was $2x + 5y = 10$?
2. How can you graph the line $3x - 2y = 10$ using the intercepts?
3. What is the slope of the line $3x - 2y = 10$?
4. How do you find the slope-intercept form of a line from its general form like $3x - 2y = 10$?
5. What happens to the intercepts if the equation involves a negative constant on the right-hand side?

Tip: To find intercepts, always set one variable to 0 and solve for the other. It makes the process quicker and easier!