How to Graph the Solution Set of an Inequality with Two Variables (Dotted Line Example)

TL;DR

Learn how to graph the solution set of an inequality by finding intercepts, using a dotted line for strict inequalities, and shading the relevant region.

Transcript

in this problem we're going to graph the solution set of this inequality so solution so the first step in this problem is to graph the equation so graph the equality so graph the equality so pretend they're equal and give a rough sketch of the graph so we have 4x equals 3y plus 12. and so i think for me the easiest way to graph this or an easy way ... Read More

Key Insights

• 📈 Graphing the solution set of an inequality involves graphing the corresponding equation and finding intercepts.
• ❣️ To find the x-intercept, set y = 0, and to find the y-intercept, set x = 0.
• 🫥 Use a dotted line for strict inequalities and a solid line for inequalities with "equal to."
• 🫥 Pick a test point not on the line to determine which region to shade.
• 😫 The shaded region represents the solution set of the inequality.
• 🫥 Using (0,0) as the test point is convenient if the line does not pass through the origin.
• 🆘 The process helps visualize the inequality and understand the region it represents.

Questions & Answers

Q: What is the first step in graphing an inequality?

The first step is to graph the corresponding equation and create a rough sketch of the graph.

Q: How do you find the intercepts?

To find the intercepts, set one variable equal to zero and solve for the other variable. The x-intercept is found by setting y = 0, and the y-intercept is found by setting x = 0.

Q: How do you determine whether to use a dotted or solid line?

For strict inequalities (e.g., <, >), use a dotted line. For inequalities with "equal to" (e.g., ≤, ≥), use a solid line.

Q: How do you determine which region to shade?

Choose a test point that is not on the line, such as (0,0), and plug it into the original inequality. If the inequality is true, shade the region where you picked the point from. If false, shade the other region.

Summary & Key Takeaways

• The first step in graphing an inequality is to graph the corresponding equation and give a rough sketch of the graph.

• To find intercepts, set one variable equal to zero and solve for the other variable.

• Test a point not on the line to determine which region to shade, based on whether the inequality is true or false.