Graphing Systems of Inequalities

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
• 0
• 1
• -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
• No

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.

• A
• B
• C
• D

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

• No

• 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

• A
• B
• C
• D

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