Graphing Linear Inequalities Concepts

The video tutorial explains how to graph a linear inequality, specifically 2X + y < 6. It begins by solving for y to convert the inequality into a form suitable for graphing. The instructor then discusses how to graph the corresponding linear equation, identifying the slope and y-intercept. The video covers how to determine whether the line should be dashed or solid and where to shade on the graph. The instructor uses test points to confirm the correct shading area and concludes with tips for ensuring accuracy in graphing linear inequalities.

What is the first step in graphing the inequality 2X + y < 6?

• Graph the line directly.

• Shade the graph.

• Solve for x.

• Solve for y.

When solving for y in the inequality 2X + y < 6, what operation is performed?

• Subtract 2x from both sides.

• Multiply both sides by 2.

• Divide both sides by 2.

• Add 2x to both sides.

What happens to the inequality sign when you multiply or divide by a negative number?

• It flips direction.

• It disappears.

• It stays the same.

• It becomes an equal sign.

What is the purpose of solving the inequality for y?

• To determine the slope.

• To eliminate the variable x.

• To graph the inequality easily.

• To find the x-intercept.

What is the y-intercept of the line y = -2x + 6?

• 6

• 2

• -2

• 0

How is the slope of a line typically represented?

• As a whole number.

• As a decimal.

• As a fraction.

• As a percentage.

What is the slope of the line y = -2x + 6?

• -2

• -1

• 2

• 1

What does the y-intercept represent on a graph?

• The steepness of the line.

• The slope of the line.

• Where the line crosses the y-axis.

• Where the line crosses the x-axis.

What is the significance of the slope in a linear equation?

• It indicates the direction and steepness of the line.

• It shows where the line crosses the x-axis.

• It is used to find the test point.

• It determines the y-intercept.

If the slope is -2, how can it be represented as a fraction?

• 2/-1

• 1/-2

• -1/2

• -2/1