Graphing the Intersection of Regions 1

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Question 1 of 4

1. Question
Graph the intersection of regions:

$y≤2-x$

$y>x$
- 1.
- 2.
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- 4.
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Remember the following notations when graphing inequalities.

Symbol Solid / Dotted

$<$ Dotted Line

$>$ Dotted Line

$≤$ Solid Line

$≥$ Solid Line

First, treat the inequality sign as an equals sign and plot the curve.

Graph the line $y=x$

Use a test point to see which side of the line is to be shaded. We can try $($ $-2$ $,$ $0$ $)$

$y$ $>$ $x$

$0$ $>$ $-2$ Substitute $(-2,0)$

The inequality is true, so we will shade the side of the line which includes the point $(-2,0)$

Next, graph the line $y=2-x$

Use a test point to see which side of the line is to be shaded. We can try the origin, $($ $0$ $,$ $0$ $)$

$y$ $≤$ $2-$ $x$

$0$ $≤$ $2-$ $0$ Substitute $(0,0)$

$0$ $≤$ $2$

The inequality is true, so we will shade the side of the line which includes the origin

Finally, shade the overlapping regions.
Question 2 of 4

2. Question
Graph the intersection of regions

$2x+3y≤6$

$x<1$
- 1.
- 2.
- 3.
- 4.
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Remember the following notations when graphing inequalities.

Symbol Solid / Dotted

$<$ Dotted Line

$>$ Dotted Line

$≤$ Solid Line

$≥$ Solid Line

First, treat the inequality sign as an equals sign and plot the curve.

Graph the line $x=1$

Since $x<1$ , we can determine that the shaded part would be the left side because all values on the left side are less than $1$

Next, graph the line $2x+3y=6$

Use a test point to see which side of the line is to be shaded. We can try the origin, $($ $0$ $,$ $0$ $)$

$2$ $x$ $+3$ $y$ $≤$ $6$

$2($ $0$ $)+3($ $0$ $)$ $≤$ $6$ Substitute $(0,0)$

$0$ $≤$ $6$

The inequality is true, so we will shade the side of the line which includes the origin

Finally, shade the overlapping regions.
Question 3 of 4

3. Question
Graph the intersection of regions

$y≥x^2$

$x+y<2$
- 1.
- 2.
- 3.
- 4.
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Remember the following notations when graphing inequalities.

Symbol Solid / Dotted

$<$ Dotted Line

$>$ Dotted Line

$≤$ Solid Line

$≥$ Solid Line

First, treat the inequality sign as an equals sign and plot the curve.

Graph the line $x+y=2$

Use a test point to see which side of the line is to be shaded. We can try the origin, $($ $0$ $,$ $0$ $)$

$x$ $+$ $y$ $<$ $6$

$0$ $+$ $0$ $<$ $6$ Substitute $(0,0)$

$0$ $<$ $6$

The inequality is true, so we will shade the side of the line which includes the origin

Next, graph the curve $y=x^2$

Use a test point to see which side of the line is to be shaded. We can try the point $($ $0$ $,$ $2$ $)$

$y$ $≥$ $\color{#9a00c7}{x}^2$

$2$ $≥$ $\color{#9a00c7}{0}^2$ Substitute $(0,0)$

$2$ $≥$ $0$

The inequality is true, so we will shade the side of the line which includes the point $(0,2)$

Finally, shade the overlapping regions.
Question 4 of 4

4. Question
Graph the intersection of regions

$x>-1$

$y≤2x-1$
- 1.
- 2.
- 3.
- 4.
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Remember the following notations when graphing inequalities.

Symbol Solid / Dotted

$<$ Dotted Line

$>$ Dotted Line

$≤$ Solid Line

$≥$ Solid Line

First, treat the inequality sign as an equals sign and plot the curve.

Graph the line $x=-1$

Since $x> -1$ , we can determine that the shaded part would be the right side because all values on the right side are greater than $-1$

Next, graph the line $y=2x-1$

Use a test point to see which side of the line is to be shaded. We can try the origin, $($ $0$ $,$ $0$ $)$

$y$ $≤$ $2$ $x$ $-1$

$0$ $≤$ $2($ $0$ $)-1$ Substitute $(0,0)$

$0$ $≤$ $-1$

The inequality is false, so we will shade the side of the line which does not include the origin

Finally, shade the overlapping regions.

Graphing the Intersection of Regions 1

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1. Question

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2. Question

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3. Question

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4. Question

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Quizzes

$y$	$≤$	$2-$ $x$
$0$	$≤$	$2-$ $0$	Substitute $(0,0)$
$0$	$≤$	$2$

$2$ $x$ $+3$ $y$	$≤$	$6$
$2($ $0$ $)+3($ $0$ $)$	$≤$	$6$	Substitute $(0,0)$
$0$	$≤$	$6$

$x$ $+$ $y$	$<$	$6$
$0$ $+$ $0$	$<$	$6$	Substitute $(0,0)$
$0$	$<$	$6$

$y$	$≥$	$\color{#9a00c7}{x}^2$
$2$	$≥$	$\color{#9a00c7}{0}^2$	Substitute $(0,0)$
$2$	$≥$	$0$

$y$	$≤$	$2$ $x$ $-1$
$0$	$≤$	$2($ $0$ $)-1$	Substitute $(0,0)$
$0$	$≤$	$-1$

Symbol	Solid / Dotted
$<$	Dotted Line
$>$	Dotted Line
$≤$	Solid Line
$≥$	Solid Line

$y$	$>$	$x$
$0$	$>$	$-2$	Substitute $(-2,0)$

Symbol	Solid / Dotted
$<$	Dotted Line
$>$	Dotted Line
$≤$	Solid Line
$≥$	Solid Line

Symbol	Solid / Dotted
$<$	Dotted Line
$>$	Dotted Line
$≤$	Solid Line
$≥$	Solid Line