Question

b) analyze the properties and complete the inequality.

boundary line	shaded region	inequality
dashed	above	$y \square -9x - 2$
solid	above	$y \square 4$
dashed	below	$y \square 10x + 1$
dashed	above	$y \square -5x + 6$

Explanation:

Step1: Solid line, below region

For a solid boundary line, we use $\leq$ or $\geq$. Shading below $y=-3x+7$ means $y$ is less than or equal to the line: $y \leq -3x + 7$

Step2: Dashed line, above region

For a dashed boundary line, we use $<$ or $>$. Shading above $y=-9x-2$ means $y$ is greater than the line: $y > -9x - 2$

Step3: Solid line, above region

Solid line uses $\leq$ or $\geq$. Shading above $y=4$ means $y$ is greater than or equal to 4: $y \geq 4$

Step4: Dashed line, below region

Dashed line uses $<$ or $>$. Shading below $y=10x+1$ means $y$ is less than the line: $y < 10x + 1$

Step5: Dashed line, above region

Dashed line uses $<$ or $>$. Shading above $y=-5x+6$ means $y$ is greater than the line: $y > -5x + 6$

Answer:

1. $y \leq -3x + 7$
2. $y > -9x - 2$
3. $y \geq 4$
4. $y < 10x + 1$
5. $y > -5x + 6$