To find the x-intercept and y-intercept of the given line equation:

$6x + 2y = -6$

Finding the x-intercept:

• At the x-intercept, y = 0.
• Substitute $y = 0$ into the equation:

$6x + 2(0) = -6 \implies 6x = -6$

• Solve for $x$:

$x = \frac{-6}{6} = -1$

So, the x-intercept is $(-1, 0)$.

Finding the y-intercept:

• At the y-intercept, x = 0.
• Substitute $x = 0$ into the equation:

$6(0) + 2y = -6 \implies 2y = -6$

• Solve for $y$:

$y = \frac{-6}{2} = -3$

So, the y-intercept is $(0, -3)$.

Summary:

• x-intercept: $(-1, 0)$
• y-intercept: $(0, -3)$

Would you like more details or further clarification?

Here are 5 related questions you can explore:

1. How do you find the intercepts of a more complex equation like $3x^2 + 2y = 10$?
2. How would the intercepts change if the equation was in slope-intercept form $y = mx + b$?
3. What is the geometric interpretation of the x- and y-intercepts on a graph?
4. How do you graph a line using just the intercepts?
5. How can you find intercepts when dealing with inequalities like $6x + 2y \geq -6$?

Tip: When finding intercepts, remember that each intercept occurs when the other variable equals zero!