Graphing Linear Inequalities Practice

Practice Objectives

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.

Problem:

Correct!

Not Correct!

Your answer was: 0

The correct answer was: 0

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