Graphing Inequalities in Slope-Intercept

Graphing Inequalities

By Angela Miller

​Next we look at the sign

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​​First Choose

Solid or Dashed Line​

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​Next we look at the sign

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​​Second Decide

Shade above or Below the line​

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​Next we look at the sign

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​​First Choose

Solid or Dashed Line​

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​Next we look at the sign

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​​Second Decide

Shade above or Below the line​

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Draw

Lets get some practice. Draw your line (solid or dashed) and shade the area (above or below)

Draw

Draw the line (solid or dashed) and shade (above or below)

Draw

Draw the line (solid or dashed) and shade (above or below)

Draw

Graph the line (solid or dashed) and shade (above or below)

Draw

Graph the line (solid or dashed) and shade (above or below)

Draw

Graph the line (solid or dashed) and shade (above or below)

When you have two equations all you have to do is graph and shade one at a time!

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Lets do this one together.

​Shade and graph at the same time to prevent confusion.

​Graphing a system of inequalities

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Plot your points

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​Shade and graph at the same time to prevent confusion.

​Graphing a system of inequalities

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Determine if its

SOLID or DASHED

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​Shade and graph at the same time to prevent confusion.

​Graphing a system of inequalities

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Determine if its Shaded

ABOVE or BELOW​

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​Shade and graph at the same time to prevent confusion.

​Graphing a system of inequalities

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Now that the first equation is graphed and shaded we look at the second one.

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Graph your points then determine if its a solid or dashed line​

​Shade and graph at the same time to prevent confusion.

​Graphing a system of inequalities

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As you shade the second equation you will see a portion of it crosses over.

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This cross over is your answer. It shows where the solution is correct for both equations.

​Shade and graph at the same time to prevent confusion.

​Graphing a system of inequalities

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Lets look at one more together.

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We must put this in y intercept format

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y=mx+b​

​Shade and graph at the same time to prevent confusion.

​Graphing a system of inequalities

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Be careful not to add or subtract these two different items

​Graphing a system of inequalities

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​Graphing a system of inequalities

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​Graphing a system of inequalities

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​y intercept is -1

slope is -3/2 or 3/-2

Plot your points and determine solid or dashed line​

​Shade and graph at the same time to prevent confusion.

​Graph and shade the first equation before you move to the second.

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​Look at your sign and determine if you are shading above or below the line

​Shade and graph at the same time to prevent confusion.

​Graph and shade the first equation before you move to the second.

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Now lets put the other equation in y intercept format so we can graph it.

​Graphing a system of inequalities

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​y intercept is 1

slope is -1/2 or 1/-2

Plot your points and determine solid or dashed line​

​Shade and graph at the same time to prevent confusion.

​Graph and shade the first equation before you move to the second.

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​Look at your sign and determine if you are shading above or below the line

​Shade and graph at the same time to prevent confusion.

​Graph and shade the first equation before you move to the second.

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• ​Your saying that the area shaded in red are all the possibilities for y for the first equation.

• The total area in blue is all the possibilities for the second equation.

• And the area that is shaded in both the blue and red are the possibilities that are valid for both equations at the same time!​

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​Shade and graph at the same time to prevent confusion.

​Where the two cross over that is your answer

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Draw

Graph the two equations and shade the areas

Use two colors

Draw

Graph the two equations and shade the areas

Use two colors

• ​Lets look at them one at a time.

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​These will create straight lines.

​Shade and graph at the same time to prevent confusion.

​What do you do if it is just x or just y?

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• ​for x < or = to 2 - we would plot a point on X at 2 then draw a solid vertical line

• Since it is < we will shade toward the negative

• This is saying that no mater what y is x will always be less than or equal to 2

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​Shade and graph at the same time to prevent confusion.

​What do you do if it is just x or just y?

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• ​for y > -1 - we would plot a point on Y at -1 then draw a solid horizontal line

• Since it is > we will shade toward the Positive

• This is saying that no mater what x is y will always be grater than but NOT equal to -1

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​Shade and graph at the same time to prevent confusion.

​What do you do if it is just x or just y?

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• ​The part shaded by both colors is the solution to the system (both equations)

​Shade and graph at the same time to prevent confusion.

​What do you do if it is just x or just y?

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Draw

Graph the two equations and shade the areas

Use two colors

Draw

Graph the two equations and shade the areas

Use two colors

Draw

Graph the two equations and shade the areas

Use two colors

Draw

Put the first equation in y intersept format

Then graph the two equations and shade the areas

Use two colors

When solving for y to put an equation in slope intercept format if you divide by a negative you must flip the sign.

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​Some text here about the topic of discussion.

​Final Concept

Your almost done!​

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Draw

Convert to y intercept form

Graph and shade the equation

Remember if you have to divide by a negative you need to flip the sign.