How to Graph Linear Functions on a TI-84 (Any Form)

Graphing a line that’s already in y = mx + b form is the easy part. Where students actually get stuck is everything before that an equation in standard form that won’t type directly into Y=, or two points with no equation given at all. This guide covers both of those, along with the basic slope-intercept case.

Does this apply to your TI-84?

Yes, TI-84, TI-84 Plus, and TI-84 Plus CE all graph linear functions identically.

Graphing from slope-intercept form (the straightforward case)

Example: graph y = 2x − 1

Press Y=
Type 2X-1 next to Y₁
Press GRAPH
If nothing appears, press ZOOM, then 6: ZStandard, to reset the window

Graphing from standard form (Ax + By = C)

This is where a lot of graphing mistakes actually start. The Y= screen expects an isolated y typing 2X+3Y=6 directly produces a syntax error, since the calculator doesn’t solve equations for you on that screen.

Example: graph 2x + 3y = 6

Rearrange to isolate y: subtract 2x from both sides to get 3y = -2x + 6, then divide everything by 3: y = (-2/3)x + 2
Press Y= and type (-2/3)X+2 keep the fraction in parentheses so it’s read as one coefficient, not split across the term
Press GRAPH

If you’d rather not do the algebra by hand, you can also enter both sides of the original equation separately (Y₁ = the left side divided out, or use the intersection method approach for solving) but for graphing specifically, isolating y first is the more reliable path.

Graphing from two points (no equation given)

This case isn’t covered in most calculator guides, but it comes up constantly in coursework you’re given two points and asked to graph the line through them.

Example: graph the line through (1, 3) and (4, 9)

Find the slope by hand first: m = (9 − 3)/(4 − 1) = 6/3 = 2
Find the y-intercept using point-slope form with either point: y − 3 = 2(x − 1), which simplifies to y = 2x + 1
Enter 2X+1 next to Y₁ and graph as usual

If you want the calculator to help with the slope calculation itself rather than doing it by hand, you can type (9-3)/(4-1) directly on the home screen to confirm the value before building the equation.

How do I check that my graphed line actually passes through the points I intended?

Use the table feature to confirm specific coordinates match your line without needing to trace visually. The table guide covers this in full, but briefly: press 2nd, then GRAPH (TABLE), and scroll to the x-values you care about the corresponding y-values should match your original points.

How do I compare two lines parallel, perpendicular, or neither?

Enter both equations in Y₁ and Y₂ and graph them together. Visually judging “perpendicular” on a standard window can be misleading, since the x and y axes aren’t equally scaled by default use ZSquare from the ZOOM menu to correct the scale before judging whether lines are actually perpendicular by eye. For a reliable check without relying on visuals at all, compare the slopes directly: equal slopes mean parallel; slopes that are negative reciprocals of each other (like 2 and −1/2) mean perpendicular.

Common mistakes and how to fix them

Typing standard form directly into Y=. The calculator can’t graph 2X+3Y=6 as written isolate y first, or the entry will throw a syntax error.

Splitting a fraction coefficient across a term. y = -2/3x + 2 typed exactly like that reads as (-2/3)·x, which is actually correct in this case, but it’s easy to accidentally produce -2/(3x) with a different equation structure. When in doubt, wrap the coefficient in parentheses: (-2/3)X.

Judging slope visually without checking scale. A standard (non-square) window can make a line look steeper or shallower than its actual slope. Compare the numeric slope values instead of trusting the visual angle, especially for parallel/perpendicular checks.

Leaving old lines active in Y=. Multiple graphed lines from earlier problems make it hard to identify which line is the current one clear or deactivate unused equations before graphing a new one.

Practice both starting points

The TI-84 Calculator Tool on this site handles slope-intercept entry the same way as the physical calculator, which makes it a good place to practice converting standard-form equations before relying on it during a timed assignment.

FAQ

Can a TI-84 graph an equation in standard form (Ax + By = C) directly?

No, the Y= screen requires an isolated y. Rearrange the equation to y = mx + b form first, then enter it.

How do I graph a line if I only have two points, not an equation?

Calculate the slope by hand (or on the home screen) using m = (y₂−y₁)/(x₂−x₁), then use point-slope form to find the y-intercept before entering the equation in Y=.

How can I tell if two lines are actually perpendicular, not just close to it visually?

Compare their slopes numerically perpendicular lines have slopes that are negative reciprocals of each other (like 2 and −1/2). Visual judgment on a non-square window can be misleading.

Why does my line look different from what I expected after graphing?

Check that a fraction coefficient wasn’t split incorrectly (wrap it in parentheses), and confirm the window includes the region where your intended points fall.