Practice Objectives

- Demonstrate the ability to graph a linear inequality in two variables
- Demonstrate the ability to find the correct inequality based on the graph

## Practice Graphing a Linear Inequality in Two Variables

Instructions:

Answer 7/10 questions correctly to pass.

Find the values for a, b, c, and the inequality symbol that matches the given graph.

Note: For this exercise, we will observe the following rules.

- a ≥ 0
- a, b, and c are integers
- a and b are not both zero
- The GCF of a, b, and c is 1

Problem:

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Graphing a Linear Inequality in Two Variables:

- Solve the inequality for y
- Find the boundary line
- Replace the inequality with an equality and graph the line
- Use the y-intercept (0, b) to plot one point
- Use the slope m, which is rise/run to plot an additional point
- For a strict inequality, we use a dashed line
- For a non-strict inequality, we use a solid line

- Shade the solution region
- The solution region lies above the boundary line for > or ≥
- The solution region lies below the boundary line for < or ≤

Finding the Inequality from its Graph:

- Locate the y-intercept
- Find the slope using rise/run or via the slope formula
- Find the equation of the boundary line
- $$y = mx + b$$
- m is the slope of the boundary line (rise/run)
- The y-int of the boundary line occurs at (0, b)

- Observe the type of line used
- If the boundary line is dashed, we have a strict inequality (< or >)
- If the boundary line is solid, we have a non-strict inequality (≤ or ≥)

- Observe the shaded region of the coordinate plane
- The shaded region represents the solution region
- If the shaded region lies below the boundary line we have a < or ≤
- If the shaded region lies above the boundary line we have a > or ≥

- Convert the inequality into the form:
- $$ax + by < c$$
- Where < represents the appropriate inequality symbol

Step-by-Step:

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Your answer should be a number!

$$a = $$

$$b = $$

$$c = $$

Inequality Symbol:

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