Graphing Linear Inequalities: Intercept Method Insights

The video tutorial explains how to graph linear inequalities in standard form using graph paper. It covers the differences between equations and inequalities, focusing on boundary lines and shading. The tutorial provides step-by-step instructions for graphing specific inequalities, including finding x and y intercepts, determining the type of boundary line, and shading the correct region. It emphasizes the importance of checking the solution by substituting a test point.

What is the primary difference between a linear equation and a linear inequality in standard form?

• The type of numbers used

• The symbols of equality or inequality

• The method of graphing

• The use of variables

What does a solid boundary line in a graph of an inequality indicate?

• The line does not include any solutions

• The inequality is less than

• The line includes the solutions

• The inequality is not equal to

How do you find the x-intercept when graphing an inequality?

• Divide the constant by the coefficient of y

• Cover the y-term and solve for x

• None of the above

• Multiply the coefficients of x and y

In the inequality 3x - 4y > 12, where should the shading be applied?

• Above the boundary line

• Below the boundary line

• On the boundary line

• No shading is needed

How do you verify if a point is in the solution set of an inequality?

• Substitute the point into the inequality

• Use a graphing calculator

• Check if the point lies on the boundary line

• Estimate the location of the point

What is the x-intercept of the inequality 5x + 6y >= -30?

• x = -5

• x = -6

• x = 6

• x = 5

For the inequality 5x + 6y >= -30, in which direction should the graph be shaded?

• Upward

• Downward

• No shading

• Shading on the line only

What type of boundary line is used for the inequality -8x + 7y > 56?

• Solid line

• No line

• Dashed line

• Both solid and dashed

In the context of the inequality -8x + 7y > 56, which way should the graph be shaded?

• Shading on the line only

• Upward

• Downward

• No shading

When graphing the inequality 2x - 9y < 18, what is the y-intercept?

• y = 9

• y = -9

• y = -2

• y = 2