How to Connect Two Points on Desmos: Lines, Segments, and Curves Explained

Desmos is one of the most accessible graphing tools available, but connecting two specific points isn't always obvious — especially since Desmos works through equations rather than click-and-drag drawing. Understanding how Desmos renders connections between points changes how you approach the problem entirely.

What "Connecting Two Points" Actually Means in Desmos

Desmos doesn't have a built-in "draw a line between these two points" button. Instead, it interprets mathematical expressions and plots them. To connect two points visually, you need to express that connection as an equation, function, or list that Desmos can render.

This means the method you use depends on what kind of connection you want:

• A straight line segment between exactly two coordinates
• An infinite line passing through two points
• A curve (quadratic, parametric, etc.) between two points
• A table-based polyline connecting a series of plotted points

Each approach uses a different Desmos feature.

Method 1: Using a Table to Plot and Connect Points 📊

The most beginner-friendly method for connecting two specific points is the table feature.

1. Click the "+" button in the expression panel and select Table
2. Enter your two x-values in the x-column and corresponding y-values in the y-column
3. Desmos will plot both points automatically

By default, the table plots points only. To connect them with a line:

• Click the colored circle next to the table
• Toggle on the lines option

This draws a straight segment directly between the plotted points. If you add more rows to the table, Desmos connects each consecutive pair — making this method ideal for polygons, paths, or piecewise shapes.

Key behavior to know: the line drawn through a table connects points in the order they appear, not by position. Order your rows intentionally.

Method 2: Writing the Line Equation Through Two Points

If you want a mathematically precise connection — especially for academic or STEM work — the equation method gives you full control.

Given two points (x₁, y₁) and (x₂, y₂), calculate the slope:

m = (y₂ − y₁) / (x₂ − x₁)

Then write the equation in point-slope form:

y − y₁ = m(x − x₁) 

Type this directly into a Desmos expression line. Desmos will render the full infinite line passing through both points.

To restrict it to a segment between only those two x-values, use Desmos's domain restriction syntax:

y − y₁ = m(x − x₁) {x₁ ≤ x ≤ x₂} 

The curly braces tell Desmos to plot only within that x-range, effectively clipping the line into a segment. 🎯

Important note: domain restrictions work cleanly for non-vertical lines. For a vertical segment (where x is constant), use:

x = 3 {y₁ ≤ y ≤ y₂} 

Method 3: Parametric Equations for More Complex Connections

When your two points need to be connected by a curve rather than a straight line — or when you want precise control over direction and path — parametric mode is the most flexible approach.

In Desmos, switch to parametric by entering an expression in the form:

(x(t), y(t)) 

For a straight segment from point A to point B, a parametric line looks like:

(x₁ + t(x₂ − x₁), y₁ + t(y₂ − y₁)) 

Set the domain as {0 ≤ t ≤ 1} and Desmos renders exactly the segment between your two points, regardless of orientation.

Parametric equations also let you define the path itself — arc, curve, or spiral — rather than accepting a straight line. This matters in projects involving animation, geometry demonstrations, or design work.

Comparing the Three Main Methods

Variables That Affect Which Method Works Best

The "right" approach shifts based on several factors:

Purpose of the graph — A student plotting geometry proofs has different needs than someone building an animated Desmos art project. Tables suit quick visual tasks; parametric suits precision and creativity.

Number of points — Connecting two points is simple. Connecting ten points in a specific path changes the equation approach from practical to tedious — the table method scales better.

Type of connection — Straight segments, Bezier-style curves, and arcs each require different mathematical representations. Desmos doesn't natively support Bezier curves, so complex curved connections require parametric workarounds or approximations.

Your comfort with equation syntax — Domain restrictions and parametric notation have a learning curve. The table method requires almost none, but offers less mathematical precision.

Device and interface — Desmos behaves consistently across browsers and the mobile app, but entering curly-brace syntax on a mobile keyboard is noticeably more friction-heavy than on desktop.

A Note on Point Labels and Intersections

Desmos also lets you define points as variables using the expression panel. For example:

A = (2, 5) B = (7, 1) 

Once defined, these can be referenced in other expressions, making it easier to update both the points and any connecting lines simultaneously — a useful workflow when exploring geometric relationships dynamically.

Whether you're building a simple two-point segment or a multi-node path, the connection between your goal and the method that serves it best comes down to how you've set up your graph, what the output needs to communicate, and how much mathematical structure the project actually requires.