Graphing Linear Inequalities Concepts

Jordan and Derek teach how to solve systems of linear inequalities. They start with an example problem, convert inequalities to slope-intercept form, and graph them. The video explains line types and shading, checks solutions, and demonstrates writing inequalities from graphs.

What is the first step in solving systems of linear inequalities?

• Graph the inequalities

• Convert to slope-intercept form

• Find the y-intercept

• Shade the solution area

Which of the following is the correct slope-intercept form of the inequality 2x - y ≤ 4?

• y ≥ 2x + 4

• y ≤ 2x - 4

• y ≥ -2x + 4

• y ≤ -2x - 4

When graphing an inequality, what type of line is used for 'greater than or equal to'?

• Solid line

• No line

• Dotted line

• Dashed line

In the context of graphing inequalities, what does shading above the line represent?

• Less than

• None of the above

• Greater than

• Equal to

How can you verify if a point is a solution to a system of inequalities?

• By graphing the point

• By finding the intercept

• By checking the slope

• By substituting the point into the inequalities

What is the result of substituting x = -2 and y = 5 into the inequality y > 0?

• The inequality is true

• The inequality is false

• The inequality is undefined

• The inequality is equal

What is the first step in writing a system of inequalities from a graph?

• Draw the lines

• Find the slope

• Find the intercept

• Shade the graph

Which of the following inequalities represents a line with a slope of -2/3?

• y < 2/3x - 4

• y > 2/3x + 4

• y ≤ -2/3x - 4

• y ≥ -2/3x + 4

What type of line is used for the inequality y < x - 3?

• No line

• Dotted line

• Dashed line

• Solid line

In the inequality y ≤ -2/3x - 4, what does the -4 represent?

• X-intercept

• Solution

• Slope

• Y-intercept