Understanding and Graphing Linear Inequalities

What is the general form of a linear inequality in two variables?

• ax + by ≥ c

• ax + by ≤ c

• ax + by < c

• ax + by = c

Which of the following is NOT a possible inequality sign in a linear inequality?

• <

• =

• >

• ≤

How can you verify if a point is a solution to the inequality y ≥ -2x + 1?

• By checking if the point lies on the line y = -2x + 1

• By solving the inequality for the point

• By substituting the point into the inequality and checking if the inequality holds

• By graphing the inequality and seeing if the point is in the shaded region

What is the first step in graphing the inequality x - y ≥ 2?

• Shade the region above the line

• Convert the inequality to an equation and graph the line

• Find the x-intercept and y-intercept

• Use a test point to determine the shading

Why is it important to use a test point when graphing inequalities?

• To verify the equation of the line

• To calculate the intercepts

• To find the slope of the line

• To determine which side of the line to shade

What does a dashed line indicate when graphing an inequality?

• The inequality is non-strict (e.g., ≤ or ≥)

• The inequality is strict (e.g., < or >)

• The line is part of the solution

• The line is not part of the solution

If the inequality is y < 3x + 2, what type of line should be drawn?

• Solid line

• Double line

• Dashed line

• Thick line

When graphing y ≤ 3x, which of the following is true?

• The line is dashed and the region below is shaded

• The line is solid and the region above is shaded

• The line is solid and the region below is shaded

• The line is dashed and the region above is shaded

What is the slope of the line y = 3x - 2?

• 2

• 1

• 3

• -2

Which point is a valid test point for the inequality y > 2x + 1?

• (3, 0)

• (2, 5)

• (1, 1)

• (0, 0)