Graphing Linear Inequalities and Systems

Presentation

•

Mathematics

•

12th Grade

•

Medium

•

CCSS

HSA.REI.D.12, 8.EE.C.8B

Standards-aligned

Lorrin Boxx

Used 6+ times

FREE Resource

5 Slides • 29 Questions

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.}

Type response here

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)

Graphing Linear Inequalities

Show answer

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