Graphing Systems of Inequalities

Presentation

•

Mathematics

•

7th - 9th Grade

•

Hard

Joseph Anderson

FREE Resource

7 Slides • 32 Questions

M3 Graphing linear Inequalities and 2 step inequalities

Slope intercept form y=mx+b

m=slope
b=y intercept

Multiple Choice

Consider the equation:
y=-x+4
Identify the slope and y-intercept.

m=4, b=-x

m=-x, b=4

m=1, b=4

m=-1, b=4

Multiple Choice

Identify the y-intercept for the function:
y=-3x

-3

-1

Solid or Dashed/Dotted Lines

Multiple Choice

y ≤ x - 2 will have what type of line?

dashed

solid

Multiple Choice

y ≤ -3x +1 will have what type of line?

dashed

solid

Multiple Choice

y ≥ 5 will have what type of line?

dashed

solid

Multiple Choice

x ≥ 2 will have what type of line?

dashed

solid

Multiple Choice

y < 6x + 1 will have what kind of line?

dashed

solid

Multiple Choice

y < x - 2 will have what kind of line?

dashed

solid

Multiple Choice

y ≥ -2x - 2 will have what type of line

dashed

solid

Multiple Choice

Will my line be solid?
5 ≥ x

Yes

Multiple Choice

How can I tell if an inequality will have a solid line?

The symbol is less than

The symbol is greater than.

The symbol has "or equal to."

You just guess.

Vertical and Horizontal lines

X only equations/inequalities will have vertical lines (up and down)
Y only equations/inequalities will have horizontal lines (left and right)

Multiple Select

The solution set for a linear inequality was graphed as shown. Which of the following linear inequalities best represents this solution set?

y > 3

y < 3

y > 3x

y < -3x

y > 3

Multiple Choice

Select the correct graph for each inequality.

Multiple Choice

Which of the following equations match the given graph?

x ≥ -1

x ≤ -1

x > -1

x < -1

Solutions to Inequalities on a Graph

The ordered pair (x, y) must be in the shaded or true area
The ordered pair can be on the line if the line is SOLID
The ordered pair is NOT a solution if it is on the line and the line is dashed (< or >)

Multiple Choice

Is the point (3, 1) a solution for the following inequality? Choose the best answer that has the best explanation.

Yes because it is located in the shaded region.

No because it is located on the line and the line is dotted.

Yes because it is located on the line.

No because it is in the shaded region.

Multiple Choice

Which point below is NOT part of the solution set?

(0, 0)

(-5, 0)

(3, 5)

(0, -2)

Multiple Choice

Which ordered pair is a solution of the inequality?

y ≥ 4x – 5

(3, 4)

(3, 0)

(2, 1)

(1, 1)

Multiple Choice

Determine whether point A is a solution to the linear inequality that is shown.

Yes

Sometimes

Graphing linear inequalities

Check if the line is solid or dashed
Check the b value and slope of the graph.
Test (0,0) to see if the area is true

Multiple Choice

Which inequality describes this graph...

y < 3x - 2

y > 3x + 2

y < 3x + 2

y > 3x -2

Multiple Choice

This is a graph of which inequality?

y > 4x - 2

y > -2x + 4

y < -2x

y < 4X - 2

Multiple Choice

Which of the following equations match the given graph?

y ≤ -3/4 x + 3

y ≥ -3/4 x + 3

y < -3/4 x + 3

y > -3/4 x + 3

Multiple Choice

What graph matches this inequality?

Multiple Choice

What graph matches this inequality?

Solving 2 Step Inequalities

Add or Subtract First
Then Multiply or Divide
The inequality sign flips only IF the variable is Negative

Multiple Choice

11 > -3y + 2

-3 > y

-3 < y

3 > y

3 < y

Multiple Choice

x < -20

x > -20

x > 20

x < 20

Multiple Choice

Solve for u.
u/7 – 1 ≤ 1

14≥u

14≤u

u≤14

u ≤ -14

Multiple Choice

Solve and graph the inequality.
7n - 1 > 76

Multiple Choice

22 < 6c + 4

11>c

3>c

11<c

3<c

Multiple Choice

2- 3x ≤ 20

x ≥ -6

x ≤ -6

x ≤ -7

x ≥ -7

Multiple Choice

Nick had $26.50 to spend at the fair. Admission to the fair was $8.50 and rides cost $1.50 per ticket. Which inequality and solution represents how many ride tickets Nick can purchase?

8.50 + 1.50x < 26.50; Nick can purchase more than 12 tickets

8.50 + 1.50x > 26.50; Nick can purchase more than 12 tickets

8.50 + 1.50x ≤ 26.50; Nick can purchase no more than 12 tickets

8.50 + 1.50x ≥ 26.50; Nick can purchase no more than 12 tickets

Multiple Choice

Twice a certain number, increased by 5, is less than three times the same number.

2x + 5 > 3x

2x + 5 < 3x

2x + 5 ≤ 3x

2x + 5 ≥ 3x

Multiple Choice

Juan bought a soda for $2. He also bought some nachos for $3 each. Juan did not spend more than $14 on the nachos and the soda. Write an inequality can be used to find n, the number of nachos that Juan could have bought.

14≥2n+3

2+3n≤14

14-3n≤2

M3 Graphing linear Inequalities and 2 step inequalities

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