Question

graphing inequalities in two variables
match each inequality to the graph of its solution.

1. $y - 2x < 2$
2. $y \leq -3x$
3. $2y - x \geq 4$
4. $x + y > 1$

graph each inequality.

Explanation:

Step1: Rewrite to slope-intercept form

1. $y - 2x < 2 \implies y < 2x + 2$
2. $y \leq -3x$
3. $2y - x \geq 4 \implies y \geq \frac{1}{2}x + 2$
4. $x + y > 1 \implies y > -x + 1$

Step2: Identify line type/inequality

• Strict inequalities ($<, >$) use dashed lines; non-strict ($\leq, \geq$) use solid lines.
• 1,4: dashed lines; 2,3: solid lines.

Step3: Match slope/intercept to graphs

1. $y < 2x + 2$: Slope=2, y-int=2, shade below dashed line → Graph b.
2. $y \leq -3x$: Slope=-3, y-int=0, shade below solid line → Graph d.
3. $y \geq \frac{1}{2}x + 2$: Slope=$\frac{1}{2}$, y-int=2, shade above solid line → Graph a.
4. $y > -x + 1$: Slope=-1, y-int=1, shade above dashed line → Graph c.

Answer:

1. $y - 2x < 2$ → b
2. $y \leq -3x$ → d
3. $2y - x \geq 4$ → a
4. $x + y > 1$ → c