Graphing Two Variable Inequalities

Multiple Choice

For this symbol,
$$\ge$$
do you shade above or below the line?

Multiple Choice

For this symbol,
$$\le$$
is it a solid line or a dashed line?

Multiple Choice

Choose the correct inequality for this graph.

• $$y>2x-3$$

• $$y\ge2x-3$$

• $$y<2x-3$$

• $$y\le2x-3$$

Graphing Linear Inequalities

Objective: Graph linear inequalities and determine solutions.

​Graphing Equations and Inequalities

​Graphs of inequalities are similar to linear equations because they both have points on a coordinate plane and a line connecting the points. However, a linear equation is ONLY the line but an inequality extends beyond that line.

​y < -3x + 1

​Graphing Linear Inequalities

​The inequality symbol tells you to SHADE ABOVE or SHADE BELOW the line.

< or ≤ Shade BELOW 

> or ≥ Shade ABOVE 

​y ≥ -3x + 1

Multiple Choice

x + y < -1

Multiple Choice

Graph 5x - 2y < 10

Multiple Choice

Which of the following is NOT a solution to the inequality graphed below?

• (4, 3)

• (-6, 0 )

• (0, 0)

• (0, 2)

Multiple Choice

Which of the following is a solution to the inequality graphed below?

• (3, 2)

• (2, -5)

• (0, 0)

• (-9, 4)

Multiple Choice

Write the linear inequality in standard form for this situation: Ms. Savva is ordering pizzas and breadsticks for a school party and has a budget of no more than $81. An order of breadsticks costs $7 and a pizza costs $13. 

• 7x + 13y < 81
• 7x + 13y ≥ 81
• 7x + 13y ≤ 81
• 7x + 13y > 81

Multiple Choice

Write the linear inequality in standard form for this situation: In order to raise money to attend upcoming competitions, the Math Pentathalon team is selling apple cider and hot chocolate. They hope to make at least $240 by selling hot chocolate for $1 a glass and hot apple cider for $2 a glass.

• x + 2y < 240
• x + 2y > 240
• x + 2y ≤ 240
• x + 2y ≥ 240

Multiple Choice

Determine whether point (-2,-3) is a solution to the linear inequality that is shown.

• Yes

• No

• Sometimes

Multiple Choice

which equation best represents this graph?

• y < 1/2x + 1

• y < 1/2x + 2

• y >1/2x + 2

• y > 2x

Multiple Choice

Which inequality is graphed on the given coordinate plane?

• y ≤ -x + 1

• y < x + 1

• y ≥ -x + 1

Multiple Choice

Are the points on the boundary line part of the solution set or not?

• Yes, they are part of the solution set
• No, they are NOT part of the solution set

Multiple Choice

Write the linear inequality that matches the graph.

• y < 3/4x - 4

• y > 4/3x - 4

• y ≤ 4/3x - 4

• y ≥ 3/4x - 4

Multiple Choice

Is this graph shaded above or below?

• above

• below

Multiple Choice

Is this graph shaded above or below?

• above

• below

Multiple Choice

Are the points on the boundary line part of the solution set or not?

• Yes, they are part of the solution set
• No, they are NOT part of the solution set

Multiple Choice

Do I need to flip my sign?
2x - 3y  ≥ 12

• Yes
• No

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