We are tasked with finding the x-intercept and the y-intercept of the equation $x + 5y = -5$.

1. To find the x-intercept:

The x-intercept occurs when $y = 0$.

• Substitute $y = 0$ into the equation: $x + 5(0) = -5$ $x = -5$ Thus, the x-intercept is $(-5, 0)$.

2. To find the y-intercept:

The y-intercept occurs when $x = 0$.

• Substitute $x = 0$ into the equation: $0 + 5y = -5$ $5y = -5$ $y = -1$ Thus, the y-intercept is $(0, -1)$.

Answer:

• x-intercept: $(-5, 0)$
• y-intercept: $(0, -1)$

Based on the provided options, the correct answer is the last choice:

• x-intercept: $(-5, 0)$
• y-intercept: $(0, -1)$

Would you like further details or have any questions?

Here are 5 related questions to explore this concept:

1. How do you find the intercepts of a quadratic equation?
2. What is the geometric meaning of intercepts in a graph?
3. Can a line have no intercepts on the coordinate axes?
4. How do you interpret intercepts in the context of real-world problems?
5. What happens to the intercepts when the equation is in different forms (like slope-intercept form)?

Tip: Always remember to set one variable to zero when finding the intercept of the other.