Graphing Linear Inequalities: Finding Solutions from Context

The video tutorial explains how to solve a problem involving the assembly of bicycles and scooters by graphing a linear inequality on a coordinate plane. It covers the process of forming an inequality from a word problem, rewriting it in slope-intercept form, plotting points, and shading the solution region. The tutorial emphasizes understanding the context to choose the correct inequality symbol and checking solutions to ensure they fit within the constraints. The lesson concludes with a summary of the key concepts and methods used.

How many hours does it take to assemble one bicycle?

• 3 hours

• 2 hours

• 4 hours

• 1 hour

What does the phrase 'at most' imply in the context of inequalities?

• Greater than or equal to

• Greater than

• Equal to

• Less than or equal to

Which form is used to graph the inequality 3X + 2Y ≤ 40?

• Standard form

• Point-slope form

• Quadratic form

• Slope-intercept form

If an employee makes 4 bicycles, what is the maximum number of scooters they can make?

• 10

• 12

• 14

• 16

Why are only whole number solutions considered in this problem?

• Because the graph only shows whole numbers

• Because fractions are not allowed

• Because the employee cannot make partial bicycles or scooters

• Because the inequality only accepts whole numbers

What happens if an employee works more than 40 hours?

• The solution is not valid

• They can make more scooters

• They get paid overtime

• They can make more bicycles

What is the significance of the shaded region in the graph?

• It shows invalid solutions

• It shows all possible solutions

• It shows only the maximum solutions

• It shows only the minimum solutions