Question

1. $x + 3y = 0$ 12. $-4x - 8y = 24$

Explanation:

Problem 11: $x + 3y = 0$

Step1: Rewrite in slope-intercept form

Isolate $y$ to get $y = mx + b$.
$3y = -x$
$y = -\frac{1}{3}x + 0$

Step2: Identify key points

• y-intercept: When $x=0$, $y=0$ (point $(0,0)$)
• x-intercept: When $y=0$, $x=0$ (same point)
• Find a second point: Let $x=3$, then $y = -\frac{1}{3}(3) = -1$ (point $(3,-1)$)

---

Problem 12: $-4x - 8y = 24$

Step1: Simplify the equation

Divide all terms by $-4$ to simplify.
$x + 2y = -6$

Step2: Rewrite in slope-intercept form

Isolate $y$ to get $y = mx + b$.
$2y = -x -6$
$y = -\frac{1}{2}x - 3$

Step3: Identify key points

• y-intercept: When $x=0$, $y=-3$ (point $(0,-3)$)
• x-intercept: When $y=0$, $0 = -\frac{1}{2}x -3 \implies x = -6$ (point $(-6,0)$)

Answer:

1. For $x + 3y = 0$:

• Slope-intercept form: $y = -\frac{1}{3}x$
• Key points to graph: $(0,0)$ and $(3,-1)$

1. For $-4x - 8y = 24$:

• Simplified/slope-intercept form: $y = -\frac{1}{2}x - 3$
• Key points to graph: $(0,-3)$ and $(-6,0)$