Introduction to Linear Inequalities

Graphing Linear Inequalities

Let's Review Inequalities!

 $<\ >\ \le\ \ge$  

Inequality Vocabulary

Greater Than >
Greater Than or Equal to  $\ge$  

Less Than <
Less Than or Equal to $\le$  

Multiple Choice

Match the Inequality symbol:

At least

• <

• >

• ≤

• ≥

Multiple Choice

Match the Inequality symbol:

No More Than

• <

• >

• ≤

• ≥

Multiple Choice

Match the Inequality symbol:

Fewer Than

• <

• >

• ≤

• ≥

Multiple Choice

Match the Inequality symbol:

more than

• <

• >

• ≤

• ≥

Graphing Inequalities on a Number Line

Multiple Choice

What inequality does the number line graph represent

• x ≤ 4
• x ≥ -4
• x < -4
• x < 4

Multiple Choice

Match the graph with its inequality.

• a > 11

• a < 11

• a ≥ 11

• a ≤ 11

Multiple Choice

What inequality does the number line graph represent?

• x > 5
• x < −5
• x ≥ 5
• x ≥ −5

Graphing Linear Inequalities

• y > 2x - 3 is to the right.

• The inequality symbol affects if we shade above or below the line. All of the shaded area are solutions!

• The symbol also affects if the line is dashed or solid. Dashed lines are not included in the solutions, but solid lines are included.

Graphing Linear Inequalities

Multiple Choice

Which inequality symbol matches this graph?

 (Click on the picture to make it larger - check for solid/dashed and shaded above or below)

• Less Than  $$<$$  

• Less Than or Equal To  $$\le$$  

• Greater Than  $$>$$  

• Greater Than or Equal to  $$\ge$$  

Multiple Choice

Which inequality symbol matches this graph?

 (Click on the picture to make it larger - check for solid/dashed and shaded above or below)

• Less Than  $$<$$  

• Less Than or Equal To  $$\le$$  

• Greater Than  $$>$$  

• Greater Than or Equal to  $$\ge$$  

Multiple Choice

Which inequality symbol matches this graph?

 (Click on the picture to make it larger - check for solid/dashed and shaded above or below)

• Less Than  $$<$$  

• Less Than or Equal To  $$\le$$  

• Greater Than  $$>$$  

• Greater Than or Equal to  $$\ge$$  

Multiple Choice

Which inequality symbol matches this graph?

 (Click on the picture to make it larger - check for solid/dashed and shaded above or below)

• Less Than  $$<$$  

• Less Than or Equal To  $$\le$$  

• Greater Than  $$>$$  

• Greater Than or Equal to  $$\ge$$  

Multiple Choice

Which inequality symbol matches this graph?

 (Click on the picture to make it larger - check for solid/dashed and shaded above or below)

• Less Than  $$<$$  

• Less Than or Equal To  $$\le$$  

• Greater Than  $$>$$  

• Greater Than or Equal to  $$\ge$$  

Multiple Choice

Which inequality symbol matches this graph?

 (Click on the picture to make it larger - check for solid/dashed and shaded above or below)

• Less Than  $$<$$  

• Less Than or Equal To  $$\le$$  

• Greater Than  $$>$$  

• Greater Than or Equal to  $$\ge$$  

Graphing Inequalities in Slope-Intercept Form

• The graph of  $y<\frac{2}{3}x-4$  is shown to the right.

• Less than (<) means dashed line, shaded below.

• Use the slope (2/3) and y-intercept (-4) to see how the inequality matches the graph.

Multiple Choice

Match the graph to the inequality. (Click on the picture to make it larger)

• y < -2x + 3

• y > -2x + 3

• y ≤ -2x + 3

• y ≥ -2x + 3

Multiple Choice

Match the graph to the inequality. (Click on the picture to make it larger)

• y < -4

• y > -4

• y ≤ -4

• y ≥ -4

Multiple Choice

Match the graph to the inequality. (Click on the picture to make it larger)

• y < 2x - 5

• y > 2x - 5

• y ≤ 2x - 5

• y ≥ 2x - 5

Multiple Choice

How would you graph the following linear inequality?

$$y\ ≤\ \frac{4}{3}x\ -\ 4$$  

• Dashed line, shade above

• Dashed line, shade below

• Solid line, shade above

• Solid line, shade below

Multiple Choice

Which graph best represents the following inequality?

Inequalities and Desmos!

Just like with regular lines, you can graph linear inequalities in Desmos. The symbols are in the keyboard! (See image on next slide)

This is helpful for any inequality, even those that are not in slope-intercept.

Multiple Choice

What graph matches this inequality? (Hint: Use desmos!)

Multiple Choice

What graph matches this inequality? (Hint: Use desmos!)

Multiple Choice

What inequality matches the graph? (Hint: Use desmos!)

Multiple Choice

What inequality matches the graph? (Hint: Use desmos!)

The end!

We will discuss more about inequlaities and their solutions after Spring Break :)