Writing Systems of Linear Inequalities from Graphs and Word Problems

This video tutorial covers how to write systems of inequalities from graphs and word problems. It explains the process of identifying inequalities from graph features such as lines and shading, and converting them to standard form. The tutorial also demonstrates how to create and solve inequalities from word problems, using examples like Tyler's cookout and Erica's shopping scenario. The video emphasizes the importance of graphing to find solution sets and highlights key concepts like slope-intercept form and standard form.

What form must you start with when writing inequalities from a graph?

• Point-slope form

• Quadratic form

• Slope-intercept form

• Standard form

What does a solid line on a graph of an inequality indicate?

• The inequality does not include the line itself.

• The inequality includes the line itself.

• The inequality is only valid above the line.

• The inequality is only valid below the line.

How do you handle the inequality sign when multiplying or dividing by a negative number?

• Keep the inequality sign the same.

• Change the inequality sign.

• Remove the inequality sign.

• Replace the inequality sign with an equal sign.

What is the slope of a line that rises 3 units for every 4 units it runs?

• 3/4

• 4/3

• -3/4

• -4/3

In a word problem, if a person buys no more than 7 items in total, how would this constraint be represented in an inequality?

• x + y > 7

• x + y >= 7

• x + y <= 7

• x + y < 7

If Tyler buys more hamburgers than hot dogs, how is this inequality represented?

• y > x

• x > y

• x < y

• y < x

What does the overlapping region on a graph of two inequalities represent?

• Solutions that satisfy both inequalities

• Solutions that satisfy at least one inequality

• Solutions that do not satisfy either inequality

• Invalid solutions

What is a possible combination of items Tyler could buy if he adheres to his constraints?

• 2 hot dogs and 4 hamburgers

• 4 hot dogs and 2 hamburgers

• 5 hot dogs and 2 hamburgers

• 3 hot dogs and 3 hamburgers

How is the inequality represented if Erica wants to spend up to $200?

• 20x + 25y <= 200

• 20x + 25y = 200

• 20x + 25y < 200

• 20x + 25y > 200

What is a valid combination of shirts and pants Erica could buy under her budget constraints?

• 3 shirts and 3 pants

• 5 shirts and 1 pant

• 1 shirt and 5 pants

• 2 shirts and 4 pants