How To Graph Inequalities On TI-84 Plus – Full Step Guide With Examples

The TI 84 graphing calculator online and its other versions like TI 84 Plus and TI-84 Plus CE are powerful graphing calculator that students often rely on for algebra, precalculus, and calculus courses. One common task you might encounter is graphing inequalities. Unlike simple equations, inequalities define regions on the coordinate plane where solutions can be found, indicated by shading either above or below a line.

In this blog, we’ll walk you through a step-by-step guide on how to graph inequalities using a TI-84 Plus, complete with practical examples. By the end, you’ll feel confident using your calculator to tackle and visualize inequality problems.

What Are Inequalities?

An inequality compares two values, rather than making them equal. For example:

  • y<2x+3 → (the area below the line)
  • y≥−x+1 → (the area above or on the line)

Graphically speaking:

  • First, you’ll plot the boundary line (solid for ≤ or ≥, dotted for < or >).
  • Then, the calculator will shade the correct area that satisfies the inequality.
what are inequalities

Can You Graph Inequalities on TI-84?

Absolutely! The TI-84 Plus and TI-84 Plus CE come with the Inequality Graphing App, which is usually pre-installed on most devices, allowing you to graph inequalities. If you don’t see it, you might need to download it from the Texas Instruments website.

Step-by-Step: How to Graph Inequalities on TI-84 Plus

Here’s how to graph inequalities on the TI-84 Plus:

Step 1: Open the Inequality App 

  • Press the APPS button.
  • Scroll to INEQ (Inequality Graphing Application).
  • Hit ENTER → select option 1: Inequality Graphing.

This app expands the regular graphing features to include inequalities.

Step 2: Enter the Inequality

  • Press Y= just like you would for regular graphing.
  • Use the left arrow key on TI 84 Keyboard to choose the type of inequality.
  • Options include:
  • Options: <, ≤, >, ≥ 
  • Now, input the equation part of the inequality.
  • Illustration: To graph y<2x+3y < 2x + 3y<2x+3:
  • In Y1, select <
  • Enter 2x + 3

Step 3: Adjust the Viewing Window

Hit the WINDOW key. 

You’ll need to set the x and y intervals so you can clearly see the shaded area. 

A good starting point could be: Xmin = -10, Xmax = 10, Ymin = -10, Ymax = 10.

Step 4: Graph the Inequality

  • Now, press the GRAPH button. 
  • Your calculator will draw the boundary line.
  • Shade the area that satisfies the inequality.

For (y < 2x + 3), you’ll see the area below the line shaded.

Illustration 1: For the inequality graph y≥-x+1

  • Open the INEQ app and select Y=
  • Choose the option ≥.
  • Enter (-x + 1) and hit GRAPH.

Outcome: You’ll see a solid line for (y = -x + 1) and the area above the line will be shaded.

Illustration 2: Now, let’s say you want to graph a system of inequalities: (y > x + 2) and (y ≤ – 2x + 5).

Steps:

  • Start by selecting Y1 > and input (x + 2).
  • Then, for Year 2, choose ≤ and enter (-2x + 5).
  • Press GRAPH.

Outcome: You’ll notice two shaded regions. The solution set is where those shaded areas overlap.

Tips for Graphing Inequalities on TI-84

  • Solid vs. Dashed Lines: The calculator does this for you! Solid lines mean ≤ or ≥, while dashed lines indicate < or >.
  • Overlapping Regions: If you’re graphing a system of inequalities, the calculator will shade both areas. The solution is where they intersect.
  • Changing Shading Color (TI 84 Plus CE Graphing Calculator only): You can customize the shading colors to enhance visibility.
  • Check Points: If you’re unsure, try using a test point, such as (0,0), to verify that the shading is accurate.

Common Mistakes Students Make

  • Forgetting to Launch the App: Typically, the Y= menu doesn’t include inequalities unless you’re using the Inequality Graphing App.
  • Incorrect Window Settings: If you can’t see the shaded area, try adjusting the Xmin, Xmax, Ymin, and Ymax values.
  • Mixing Up Symbols: Just a heads up: < and > represent dashed lines, while ≤ and ≥ indicate solid lines.
  • Not Identifying Overlaps: When solving systems, only the overlapping coloured area yields the proper solution.

Conclusion

The TI-84 Plus makes graphing inequalities a breeze compared to doing it by hand. With the Inequality Graphing App, you can quickly input inequalities, shade the relevant areas, and graph multiple inequalities at once to find overlapping solution sets.

By following the step-by-step guide above, you can now:

  • Input and illustrate inequalities.
  • Create residual plots of the shaded areas.
  • Graphically solve systems of inequalities.

Mastering how to graph inequalities on the TI-84 is crucial for excelling in algebra, precalculus, and statistics courses. With practice, you’ll be able to use your calculator to check your solutions and save time on homework and tests.

FAQs for How to Graph Inequalities on TI-84 Plus

You can easily plot and shade inequality graphs with the Inequality Graphing App.

To get started, just hit the [APPS] button and then press Enter to jump to Inequality Graphing (INEQ).

Once you’re in, go to [Y=] and enter your equation, choosing from the symbols, select <, ≤, >, or ≥.

Solid = ≤ or ≥, Dashed = < or >.

Don’t forget to use the [WINDOW] key; for example, you might set Xmin to -10, Xmax to 10, and Ymin to -10, Ymax to 10.

Feel free to plug your equations into Y1, Y2, and so on; the overlapping area is where you’ll find the solutions.

If your window settings seem too small or if the Inequality app isn’t running, that could be the issue.

And hey, you can even change the shading colours on the TI-84 Plus CE!

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