Question

practice f
write an inequality for each graph. in each case, the equation for the boundary line is given.

1. y = x - 2
2. x - 2y = 4
3. y - 2x = 4
4. y = -2
5. x = 2
6. -2x - 3y = 6
7. 3x - y = 3
8. y - 3x = 3

Explanation:

1.

Step1: Identify line type

The boundary line $y=x - 2$ is dashed, so the inequality is strict.

Step2: Test a point

Test $(0,0)$. Substitute into $y-(x - 2)$: $0-(0 - 2)=2>0$. So the region containing $(0,0)$ gives $y>x - 2$.

2.

Step1: Identify line type

The boundary line $x - 2y=4$ is solid, so the inequality is non - strict.

Step2: Test a point

Test $(0,0)$. Substitute into $x-2y - 4$: $0-2\times0 - 4=-4\leqslant0$. So the region containing $(0,0)$ gives $x-2y\leqslant4$.

3.

Step1: Identify line type

The boundary line $y - 2x=4$ is solid, so the inequality is non - strict.

Step2: Test a point

Test $(0,0)$. Substitute into $y-2x - 4$: $0-2\times0 - 4=-4<0$. The region not containing $(0,0)$ gives $y-2x\geqslant4$.

4.

Answer:

$y>x - 2$