Graphing two variable inequality

TL;DR

Learn how to graph the inequality -14x -7y < 4 and shade the region above the line.

Transcript

• [Instructor] So what I would like to do in this video is graph the inequality negative 14 X minus seven Y is less than four. Like always, I encourage you to pause this video and see if you can graph it on your own before we work through it together. So the way that I like to do this is I like to isolate a Y on one side of this inequality, and I'l... Read More

Key Insights

• ❣️ Isolate the y-variable by adding the corresponding number of x from the other side of the inequality.
• ➗ Swapping the inequality sign is necessary when dividing both sides by a negative number.
• 🫥 The graph of a strict inequality is represented by a dotted line.
• 🫥 The shaded region includes all points above the line.
• 😀 The y-intercept and slope are useful in graphing the equation accurately.
• ❣️ Understanding the relationship between x and y allows for precise plotting.
• 😨 Care should be taken while swapping inequality signs to avoid errors.

Questions & Answers

Q: How should you isolate the y-variable in the inequality -14x -7y < 4?

To isolate the y-variable, you should add 14x to both sides of the inequality. This leaves you with -7y < 14x + 4.

Q: Why do you need to swap the inequality sign when dividing both sides of the inequality by -7?

When multiplying or dividing both sides of an inequality by a negative number, it is necessary to swap the inequality sign. This results in y > -2x - 4/7 instead of y < -2x - 4/7.

Q: How can the graph of the inequality -14x -7y < 4 be represented?

The graph is a dotted line because it is strictly less than. The equation y = -2x - 4/7 should be plotted, and the region above the line should be shaded.

Q: What is the significance of the y-intercept and slope in graphing the inequality?

The y-intercept helps determine the starting point on the graph, while the slope of -2 indicates that for every increase of one in x, y decreases by two, helping to plot additional points.

Summary & Key Takeaways

• The video demonstrates how to graph the inequality -14x -7y < 4 by isolating the y-variable and swapping the inequality sign when dividing by a negative number.

• The graph of the inequality is a dotted line, since it is strictly less than, and the shaded region includes all points above the line.

• By using the y-intercept and slope, the video illustrates how to plot the equation and shade the region accurately.