Let's solve the given equations to find their x-intercepts and y-intercepts.

a) $10x + 4y = 20$

• x-intercept: Set $y = 0$ and solve for $x$. $10x + 4(0) = 20 \implies 10x = 20 \implies x = 2$ The x-intercept is $(2, 0)$.

• y-intercept: Set $x = 0$ and solve for $y$. $10(0) + 4y = 20 \implies 4y = 20 \implies y = 5$ The y-intercept is $(0, 5)$.

b) $4x - 8y = -40$

• x-intercept: Set $y = 0$ and solve for $x$. $4x - 8(0) = -40 \implies 4x = -40 \implies x = -10$ The x-intercept is $(-10, 0)$.

• y-intercept: Set $x = 0$ and solve for $y$. $4(0) - 8y = -40 \implies -8y = -40 \implies y = 5$ The y-intercept is $(0, 5)$.

c) $x = -5$

This is a vertical line, so it only has an x-intercept.

• x-intercept: $x = -5$, so the intercept is $(-5, 0)$.
• y-intercept: Since it's a vertical line, there is no y-intercept.

d) $y = 3$

This is a horizontal line, so it only has a y-intercept.

• x-intercept: A horizontal line has no x-intercept.
• y-intercept: $y = 3$, so the intercept is $(0, 3)$.

Summary of the intercepts:

a) x-int: $2$, y-int: $5$
b) x-int: $-10$, y-int: $5$
c) x-int: $-5$, y-int: None
d) x-int: None, y-int: $3$

Let me know if you need more details or if you have any questions!

Here are some additional related questions to consider:

1. How do you find intercepts for non-linear equations?
2. What does the slope of a line tell us about the relationship between x and y?
3. Can a line have both intercepts equal to zero? What does that mean geometrically?
4. What is the intercept form of the equation of a line?
5. How would intercepts change if the coefficients in the equation were fractions?

Tip: Always substitute $x = 0$ for y-intercepts and $y = 0$ for x-intercepts to solve these kinds of problems easily.