How to Graph Inequalities on TI-84

How to Graph Inequalities on TI-84

A regular equation usually creates a single line on a graph, while an inequality represents a whole area of possible solutions. On the TI-84, you can graph inequalities by using different settings depending on the type of inequality. One method works for inequalities with two variables, while another can be used to show solutions on a number line. Both methods are simple once you know which settings to use.

What Is Graphing an Inequality on the TI-84?

Graphing an inequality on the TI-84 means using the calculator to show the solutions of an inequality on a coordinate graph. The TI-84 can display a boundary line and shade the area where the inequality is true. For example, inequalities such as y > x + 2 or y ≤ 2x − 1 can be entered and graphed directly. The type of inequality determines whether the boundary appears as a solid or dashed line and which side of the graph is shaded.

For more features of the calculator, check out the how to use TI-84 effectively guide.

Method 1: Using the Inequality Graphing App

This is the easiest way to graph inequalities on TI-84 for two-variable problems like ( y < 2x + 3 ). It works reliably on all app versions.

  • Press APPS and scroll to INEQ, the Inequality Graphing app.
  • Press ENTER to open it, then go to the Y= editor.
  • Use the ALPHA key to pick the right inequality symbol next to a Y slot.
  • Type the expression, like 2X + 3, after selecting the symbol.
  • Press GRAPH to see the shaded solution area.

The app chooses if the boundary line is solid or dashed. It uses solid for ( \leq ) or ( \geq ) and dashed for ( < ) or ( > ). You can enter multiple inequalities, and the overlapping shaded area shows the solution for the whole system.

Worked Example: y < 2x + 3

Walking through one full example makes the steps easier for future problems.

  • Start by opening INEQ from the APPS menu.
  • Then, go to the Y1 slot in the inequality editor.
  • Press ALPHA to cycle through the symbols until you see the less than symbol. This is important since the problem uses a strict inequality, not less than or equal to.
  • Type 2X + 3 as the expression and press GRAPH.

The screen shows a dashed line through the standard slope-intercept points. The region below the line is shaded, representing all coordinate pairs that satisfy the inequality. Pick a point like (0, 0) and check it against the original inequality: 0 < 2(0) + 3. This confirms that 0 is less than 3. So, the origin lies inside the shaded area, matching the graph.

Checking a Solution with Shades and Trace

After shading a graph, the app offers tools to check specific points. This is helpful once you understand how to graph inequalities on the TI-84. You can confirm your answer before writing it down.

  • Press ALPHA to access the Shades and PoI-Trace options at the bottom.
  • Select PoI-Trace to find points of intersection between two inequality boundaries.
  • Use the arrow keys to move the cursor and check if a point is in the shaded area.

Method 2: Graphing a One-Variable Inequality

The TI-84 doesn’t have a specific tool for one-variable inequalities like x > 3 on a number line. However, you can use Boolean logic to graph inequalities effectively. This method remains helpful when the two-variable approach feels routine.

  • Press Y= and enter the full inequality, like 1 − X > 3.
  • Press 2ND, then MATH to open the TEST menu and choose the right inequality symbol.
  • Press ZOOM, then 6, to graph in the standard window.
  • Press TRACE and enter a value to see if that point is true or false.

The calculator treats the statement as a Boolean expression, returning 1 for true and 0 for false. The graph appears as a flat line just above the x-axis, showing where the inequality is valid.

Worked Example: 1 − x > 3

  • Type 1 − X > 3 into the Y1 slot on the Y= screen.
  • Use 2ND and then MATH to add the greater than symbol from the TEST menu instead of typing it.
  • Next, press ZOOM and then 6 for the standard window. The graph will show a flat segment above the x-axis. This happens because each point on that segment returns a Boolean value of 1 or 0, not a calculated y-value.
  • Press TRACE and type −3 to check that x-value. You’ll see a y-value of 1, confirming the statement is true there.
  • Typing 0 gives a y-value of 0, showing the inequality is false at that point.

By testing a few values along the flat segment, you can find where it starts. This marks the boundary of the solution set on the number line. Fraction-heavy inequality problems often appear too, and the steps for how to do fractions on a TI-84 fit well with these methods.

Common Mistakes to Avoid

Few mistakes cause confusion for students using the TI-84 to graph inequalities.

Skipping the Inequality Symbol Selection

If you type the expression before choosing the symbol with ALPHA, the calculator misses the inequality information. This often leads to no shaded region appearing.

Misreading Solid Versus Dashed Boundaries

A solid line includes boundary points for ≤ or ≥. In contrast, a dashed line excludes them for strict inequalities like < or >.

Using the Wrong Method for One-Variable Problems

The INEQ app is for two-variable problems. For a one-variable inequality like x > 3, use the TEST menu method instead.

Rushing Past the Shaded Overlap in Systems

When multiple inequalities are graphed, only the overlapping shaded region represents the true solution. Single inequality shading does not show the complete answer.

Conclusion

You can graph inequalities on TI-84 easily. Use the Inequality Graphing app for two-variable problems. For one-variable number lines, use the TEST menu trick. Mastering both methods will help with most algebra and precalculus tasks. After practicing a few problems, switching between them will feel natural.