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Graph Linear Inequalities 1Graph Linear Inequalities 1
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Question 1 of 8
1. Question
Graph `x > 3`Hint
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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=3`
Use a test point to see which side of the line is to be shaded. We can try the origin, `(``0``,0)``x` `>` `3` `0` `>` `3` Plug in `0` as `x` The inequality is not true, so we will shade the side of the line which does not include the origin.Now we can graph the inequality.`>` means we must use a dashed line when graphing `x > 3`
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Question 2 of 8
2. Question
Graph `y ≤ 2`Hint
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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=2`
Use a test point to see which side of the line is to be shaded. We can try the origin, `(``0``,0)`.`y` `≤` `2` `0` `≤` `2` Plug in `0` as `y` The inequality is true, so we will shade the side of the line which includes the origin.Now we can graph the inequality`≤ ` means we must use a solid line when graphing `y ≤ 2`
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Question 3 of 8
3. Question
Graph `x > 4`Hint
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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=4`
Use a test point to see which side of the line is to be shaded. We can try the origin, `(``0``,0)`.`x` `>` `4` `0` `>` `4` Plug in `0` as `x` The inequality is not true, so we will shade the side of the line which does not include the origin.Now we can graph the inequality.`>` means we must use a dashed line when graphing `x > 4`
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Question 4 of 8
4. Question
Graph `y > 2x-3`Hint
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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=``2``x``-3`
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``-3` `0` `>` `2``(0)``-3` Plug in `0` as `x` and `y` `0` `>` `-3` Simplify The inequality is not true, so we will shade the side of the line which does not include the origin.Now we can graph the inequality.`>` means we must use a dashed line when graphing `y > 2x-3`
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Question 5 of 8
5. Question
Graph `y ≤ -3x+2`Hint
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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=``-3``x+``2`
Use a test point to see which side of the line is to be shaded. We can try the origin, `(``0,0``)`.`y` `≤` `-3``x``+2` `0` `≤` `-3``(0)``+2` Plug in `0` as `x` and `y` `0` `≤` `2` Simplify The inequality is true, so we will shade the side of the line which includes the origin.Now we can graph the inequality`≤ ` means we must use a solid line when graphing `y ≤ -3x+2`
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Question 6 of 8
6. Question
Graph `2x+3y > 6`Hint
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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 `2x+3y=6`Write the equation in point-gradient form.`2x+3y` `=` `6` `2x+3y``-2x` `=` `6``-2x` Subtract `2x` from both sides `3y` `=` `-2x+6` Simplify `y` `=` `-2/3x+2` Divide both sides by `3` You may now graph the line `2x+3y=6` with its gradient-intercept form.The slope of the line is `-2/3` and the y-intercept is `2`.
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` Plug in `0` as `x` and `y` `0` `>` `6` Simplify The inequality is not true, so we will shade the side of the line which does not include the origin.Now we can graph the inequality.`>` means we must use a dashed line when graphing `2x+3y > 6`
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Question 7 of 8
7. Question
Graph `x+3y-3``<``0` and `x-y+2 ≤ 0`Hint
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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+3y-3=0`Write the equation in point-gradient form.`x+3y-3` `=` `0` `x+3y-3``-x+3` `=` `0``-x+3` Add `-x+3` to both sides `3y` `=` `-x+3` Simplify `y` `=` `-1/3x+1` Divide both sides by `3` You may now graph the line `x+3y-3``<``0` with its gradient-intercept form.The slope of the line is `-1/3` and the y-intercept is `1`.
Use a test point to see which side of the line is to be shaded. We can try the origin, `(``0,0``)`.`x``+3``y``-3` `<` `0` `0``+3``(0)``-3` `<` `0` Plug `0` as `x` and `y` `-3` `<` `0` Simplify The inequality is true, so we will shade the side of the line which includes the origin.Graph the line `x-y+2=0`Write the equation in point-gradient form.`x-y+2` `=` `0` `x-y+2``-x-2` `=` `0``-x-2` Add `-x-2` from both sides `-y` `=` `-x-2` Simplify `y` `=` `x+2` Divide both sides by `-1` You may now graph the line `x-y+2 ≤ 0` with its gradient-intercept form.The slope of the line is `1` and the y-intercept is `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``+2` `≤` `0` `0``-``0``+2` `≤` `0` Plug in `0` as `x` and `y` `2` `≤` `0` Simplify The inequality is not true, so we will shade the side of the line which does not include the origin.Now we can graph the two inequalities.`<` means we must use a dashed line when graphing `x+3y-3``<``0``≤` means we must use a solid line when graphing `x-y+2 ≤ 0`
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Question 8 of 8
8. Question
Shade the region bounded by inequalities `y≥1/2x`, `y≤2` and `y``<``2x+4`Hint
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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=1/2x`The slope of the line is `1/2` and the y-intercept is `0`.
Use a test point to see which side of the line is to be shaded. We can try the origin, `(``0,0``)`.`y` `≥` `1/2``x` `0` `≥` `1/2``(0)` Plug `0` as `x` and `y` `0` `≥` `0` Simplify The inequality is true, so we will shade the side of the line which includes the origin.`≥` means we must use a solid line when graphing `y≥1/2x`
Graph the line `y=2`.
Use a test point to see which side of the line is to be shaded. We can try the origin, `(0,``0``)`.`y` `≤` `2` `0` `≤` `2` Plug `0` as `y` The inequality is true, so we will shade the side of the line which includes the origin.`≤` means we must use a solid line when graphing `y≤2`
Graph the line `y=2x+4`The slope of the line is `2` and the y-intercept is `4`.
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``+4` `0` `<` `2``(0)``+4` Plug `0` as `x` and `y` `0` `<` `4` Simplify The inequality is true, so we will shade the side of the line which includes the origin.`<` means we must use a dashed line when graphing `y``<``2x+4`
Now we can graph the three inequalities.
Quizzes
- Distance Between Two Points 1
- Distance Between Two Points 2
- Distance Between Two Points 3
- Midpoint of a Line 1
- Midpoint of a Line 2
- Midpoint of a Line 3
- Slope of a Line 1
- Slope of a Line 2
- Slope Intercept Form: Graph an Equation 1
- Slope Intercept Form: Graph an Equation 2
- Slope Intercept Form: Write an Equation 1
- Graph Linear Inequalities 1
- Convert Standard Form and Slope Intercept Form 1
- Convert Standard Form and Slope Intercept Form 2
- Point Slope Form 1
- Point Slope Form 2
- Parallel Lines 1
- Parallel Lines 2
- Perpendicular Lines 1
- Perpendicular Lines 2