Question: List the intercepts for the graph of the equation: $4x^2+16y^2=64$
1. **State the problem:** Find the intercepts of the graph of the equation $$4x^2 + 16y^2 = 64$$.
2. **Recall the intercepts:**
- The $x$-intercepts occur where $y=0$.
- The $y$-intercepts occur where $x=0$.
3. **Find the $x$-intercepts:**
Set $y=0$ in the equation:
$$4x^2 + 16(0)^2 = 64 \implies 4x^2 = 64$$
Divide both sides by 4:
$$\cancel{4}x^2 = \cancel{4}16 \implies x^2 = 16$$
Take the square root of both sides:
$$x = \pm \sqrt{16} = \pm 4$$
So, the $x$-intercepts are at points $(4,0)$ and $(-4,0)$.
4. **Find the $y$-intercepts:**
Set $x=0$ in the equation:
$$4(0)^2 + 16y^2 = 64 \implies 16y^2 = 64$$
Divide both sides by 16:
$$\cancel{16}y^2 = \cancel{16}4 \implies y^2 = 4$$
Take the square root of both sides:
$$y = \pm \sqrt{4} = \pm 2$$
So, the $y$-intercepts are at points $(0,2)$ and $(0,-2)$.
5. **Final answer:**
- $x$-intercepts: $(4,0)$ and $(-4,0)$
- $y$-intercepts: $(0,2)$ and $(0,-2)$