Graphing Linear Inequalities and Systems

Graphing Linear Inequalities

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

How would you graph the following linear inequality?

y ≥ 4

• Dashed line, shade above

• Dashed line, shade below

• Solid line, shade above

• Solid line, shade below

Multiple Choice

• y < -2x + 3 
• y > -2x + 3 
• y ≤ -2x + 3 
• y ≥ -2x + 3 

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

• y < 2x - 5
• y > 2x - 5
• y ≤ 2x - 5
• y ≥ 2x - 5

Multiple Choice

• y < 5x + 1 
• y > 5x + 1 
• y ≤ 5x + 1 
• y ≥ 5x + 1  

Multiple Choice

• y < -4 
• y > -4
• y ≤ -4 
• y ≥ -4 

Multiple Choice

• y < -x - 5
• y > -x - 5
• y ≤ -x - 5
• y ≥ -x - 5

Multiple Choice

• y < -3/4x - 2 
• y > -3/4x - 2 
• y ≤ -3/4x - 2 
• y ≥ -3/4x - 2 

Multiple Choice

• y < 3/5x - 5
• y > 3/5x - 5
• y ≤ 3/5x - 5
• y ≥ 3/5x - 5

Multiple Choice

• y < -2x + 3 
• y > -2x + 3 
• y ≤ -2x + 3 
• y ≥ -2x + 3 

Multiple Choice

• y < -2/5x - 4

• y > -2/5x - 4

• y ≤ -2/5x - 4

• y ≥ -2/5x - 4

Multiple Choice

• y < 5x + 1 
• y > 5x + 1 
• y ≤ 5x + 1 
• y ≥ 5x + 1  

Multiple Choice

• y < -2/5x - 4

• y > -2/5x - 4

• y ≤ -2/5x - 4

• y ≥ -2/5x - 4

Multiple Choice

• y < -3/4x - 2 
• y > -3/4x - 2 
• y ≤ -3/4x - 2 
• y ≥ -3/4x - 2 

Let's make them a system!

Graph both inequalities on the same coordinate plane

But wait...where is the solution?!

Solution to a System of Inequalities

Is all ordered pairs that make ALL inequalites true.

**WHERE THE SHADED PORTIONS OF THE BOTH INEQUALITIES OVERLAP.**

Steps to Graphing Systems of Inequalities

• Make sure both inequalities are in Slope-Intercept Form.

• Graph both inequalities (Don't forget to determine dashed or solid line and shade above or shade below).

• Heavily shade in the portion where the shaded regions overlap. This is the solution to the system of inequalities.

• At this point, downsize this screen and go watch the video that is also attached on Google Classroom and then come back here for the practice problems.

Poll

Where do you think the solution will be?

• Blue

• Purple

• Red

• White

• All of blue and all of red

Multiple Choice

Which of the following is a solution to the systems of inequalities?

• (-1, -3)

• (3, 0)

• (-2, 2)

• (4, 1)

Open Ended

Which area (white, red, purple, blue) do you think represents the solution to this system of inequalities? Explain your reasoning.

_{Remember that a solution makes BOTH inequalities true at the same time.}

Multiple Choice

Solve the system of inequalities by graphing.

Multiple Choice

Which of the following is NOT a solution to the systems of inequalities?

• (0, 0)

• (3, -2)

• (3, -4)

• (4, -4)

Multiple Choice

Which of the following is a solution to the systems of inequalities?

• (0, -2)

• (-3, 0)

• (-3, 2)

• (1, 1)

Multiple Choice

Solve the system of inequalities by graphing.

Multiple Choice

Which of the following is a solution to the systems of inequalities?

• (0, 0)

• (-3, 0)

• (2, -5)

• (3, -1)

Multiple Choice

Graph:
y≤-2x+5
y>2x+7
Which of the following is NOT a solution?

• (-4, 2)
• (-10, 7)
• (-3, 0)
• (-2, 6)

Multiple Choice

Solve the system of inequalities by graphing. $$8x\ +4y\ge10\ and\ 3x-6y>12$$  

Multiple Choice

Identify the graph represented by the following system of inequalities.

2x - y > 4

4x + 2y < 6

Multiple Choice

Is (-2, 0) a solution to the system?

• Solution

• Not a solution

Multiple Choice

Given the graph, determine which is NOT a solution.

• (0, 0)

• (2, -1)

• (-2, -2)

• (-5, 1)

Multiple Choice

Given the system, determine a solution.

• No solution

• Infinite solutions

• (-5, 5)

• (5, -5)