Graphing Linear Inequalities with Less Than and Less Than or Equal to Symbols

The video tutorial explains how to graph linear inequalities with less than or less than or equal to symbols. It covers the process of plotting points, drawing boundaries with solid or dotted lines, and shading regions to represent all possible solutions. The tutorial distinguishes between strict inequalities and those that include equality, emphasizing the importance of shading the correct half-plane to show solutions.

What is the first step in graphing the equation y = x - 4?

• Draw a dotted line

• Shade the region below the line

• Choose x values and find corresponding y values

• Plot only the y-intercept

When graphing y ≤ x - 4, what does the shaded region below the line represent?

• Only the boundary line

• All possible solutions to the inequality

• The x-intercept

• Solutions that are greater than the line

How is a strict inequality like y < 2x + 4 represented on a graph?

• With a solid line

• With a dotted line

• With a dashed line

• With no line at all

For the inequality y < 2x + 4, why is a dotted line used?

• To indicate the boundary is not included

• To indicate the boundary is included

• To show the line is temporary

• To highlight the x-intercept

What is the main difference between graphing y ≤ x - 4 and y < 2x + 4?

• The number of solutions

• The position of the x-axis

• The color of the shaded region

• The type of line used for the boundary

In the inequality y < -4x - 3, what does the shaded region below the dotted line represent?

• Only the x-intercept

• All possible y values less than the line

• The boundary line

• All possible y values greater than the line

What is the purpose of shading the region below the line in a graph of a linear inequality?

• To show the solutions that are not possible

• To highlight the x-intercept

• To represent all possible solutions to the inequality

• To indicate the graph is complete