(Q12) Sample #1, Math 141/146 common final, Glendale community college

TL;DR

Learn to graph linear inequalities using slope-intercept form; shade above dashed line.

Transcript

all right for number 12 we are going to graph the linear inequality 2x plus 3y is greater than 12 and this is the strategy let's isolate the y first because this way we'll be able to get the equation and in this case we have the inequality y is equal to mx plus b then we will be able to use the slope and the y-intercept to graph the line let's grap... Read More

Key Insights

• 😀 Isolating y in linear inequalities is crucial for easy graphing.
• ➗ Division by a positive number maintains the inequality sign.
• 🦻 Understanding the slope-intercept form aids in graphing accurately.
• 🟰 Dashed lines are used for inequalities without the equal sign.
• ❓ Proper shading direction signifies the solution region.
• 🆘 Y-intercept and slope help in plotting points on the graph.
• 💯 Practice makes perfect in accurately graphing linear inequalities.

Questions & Answers

Q: How do you isolate y in a linear inequality for graphing?

To isolate y in a linear inequality, first simplify the equation by moving terms to different sides.Then, divide by the coefficient of y to get it in the form y > mx + b.

Q: Why do we use a dashed line for graphing a linear inequality?

A dashed line is used for graphing linear inequalities because the inequality symbol does not include equality (not equal to). It signifies that the points on the line are not part of the solution.

Q: What does the y-intercept represent in graphing linear inequalities?

The y-intercept (4 in this case) represents the point where the line intersects the y-axis. It is used as the starting point for graphing and helps in plotting the initial point.

Q: Why do we shade above the dashed line for y > -2/3x + 4?

We shade above the dashed line because the inequality symbol is greater than which indicates the area above the line represents the solution set.

Summary & Key Takeaways

• Isolate y in the linear inequality equation 2x + 3y > 12 to graph the line.

• Divide by 3 to simplify the inequality to y > -2/3x + 4.

• Use y-intercept (4) and slope (-2/3) to graph the dashed line and shade above for the solution.