Question

1. 12x + 8y < 24
2. ≤ 1

Explanation:

Step1: Rewrite inequality 10 to slope-intercept form

Start with $12x + 8y < 24$. Subtract $12x$:
$8y < -12x + 24$
Divide by 8:
$y < -\frac{3}{2}x + 3$

Step2: Find intercepts for inequality 10

x-intercept: set $y=0$:
$12x = 24 \implies x=2$
y-intercept: set $x=0$:
$8y=24 \implies y=3$
Draw a dashed line through $(2,0)$ and $(0,3)$, shade below it.

Step3: Analyze inequality 12: $y \leq 1$

Draw a solid horizontal line at $y=1$, shade below it.

Answer:

1. For $\boldsymbol{12x + 8y < 24}$:

• Graph a dashed line with x-intercept $(2, 0)$ and y-intercept $(0, 3)$ (equation $y = -\frac{3}{2}x + 3$), then shade the region below this line.

1. For $\boldsymbol{y \leq 1}$:

• Graph a solid horizontal line at $y=1$, then shade the region below this line.