Graphing Linear Inequalities Concepts

The video tutorial explains how to graph a linear inequality, specifically X - 4Y < 4. It covers the steps to graph the borderline, which involves treating the inequality as an equation and using a dashed line. The tutorial also demonstrates how to find the x and y intercepts to graph the line and determine which side of the line to shade by using a test point. The solution area is shaded to represent all points that satisfy the inequality.

What is the first step in graphing the linear inequality X - 4Y < 4?

• Determine the y-intercept

• Find the slope of the line

• Graph the borderline

• Shade the region above the line

Why is a dashed line used for the inequality X - 4Y < 4?

• Because the inequality is strict (< or >)

• Because the inequality is non-strict (<= or >=)

• To indicate the line is part of the solution

• To make the graph look better

What is the equation of the borderline for the inequality X - 4Y < 4?

• 4X - Y = 4

• X - 4Y = 4

• X + 4Y = 4

• X - 4Y = 0

How can you find the x-intercept of the line X - 4Y = 4?

• Set X = 4

• Set Y = 0

• Set Y = 4

• Set X = 0

What are the coordinates of the y-intercept for the line X - 4Y = 4?

• (0, 4)

• (4, 0)

• (1, 0)

• (0, -1)

Which point is commonly used as a test point to determine shading?

• (1, 1)

• (0, -1)

• (0, 0)

• (4, 0)

What does it mean if the test point (0, 0) satisfies the inequality X - 4Y < 4?

• The inequality is incorrect

• The line is part of the solution

• Shade the same side as the test point

• Shade the opposite side of the line

What is the final step in graphing the inequality X - 4Y < 4?

• Draw a solid line

• Shade the correct half-plane

• Recalculate the intercepts

• Erase the test point

Which half-plane is shaded for the inequality X - 4Y < 4?

• Below the line

• Above the line

• On the line

• Neither side

What does the shaded region represent in the graph of X - 4Y < 4?

• Only the intercepts

• All points that do not satisfy the inequality

• Only the test point

• All points that satisfy the inequality