Desmos Basics: The Interface

The expression list is where you type. Each line is its own graph, so y = 2x + 3 on one line and y = -x on the next draws both at once. Desmos redraws the instant you finish typing, and you never have to press an equals or a graph button.

On a laptop, the list sits to the left of the graph, which is how it looks in Bluebook on test day. On a phone the same two panels stack, graph on top, list underneath. Nothing else changes.

You also never have to rearrange an equation first. Something like 4y = 15x - 8 graphs exactly as written, which is why so many SAT questions turn into typing and clicking.

This is the move that makes Desmos worth it. Desmos marks the important points on a graph as small gray dots: the x-intercept and y-intercept where a graph crosses an axis, the intersection point where two graphs meet, the vertex of a parabola where it turns around, and the peaks and dips of any curve. Those are exactly the points SAT questions ask for, which is why so many of them come down to selecting an equation and clicking a dot.

But Desmos only draws the dots while that graph is selected. Click inside an equation box (or on the curve itself) and they appear; click away and they hide again. Hover a dot and Desmos shows its coordinates. Click it and the point turns solid so the coordinates stay on screen. You are never eyeballing the grid; you are reading the number Desmos hands you.

If the point you need is off the screen, scroll to zoom, or use the plus and minus buttons in the top right, and drag the graph to move around. The house-shaped button under them resets the view when you have wandered off.

When a graph has data points on it, a Zoom Fit button appears too, and one click frames everything you have plotted. For a very tall or very wide window, open the wrench menu and type the axis bounds you want directly.

The wrench icon in the top right of the graph opens the settings. Two of them matter on the SAT. Radians or Degrees decides how Desmos reads an angle. Let the answer choices pick it: plain numbers like 30 or 90 mean degrees, anything with a pi in it means radians. And Display Size makes the labels and axes bigger, which is worth a click if you find yourself squinting.

One thing catches people right after the switch: in Degrees the sine wave looks flat. Nothing is wrong. The window still runs from -10 to 10, and 10 degrees is a sliver of one wave. The x-axis range is in the same menu: type -360 and 360 into the two x boxes and the wave comes back. Do the same on any trig question whose graph looks like a flat line. Both ranges are in that menu, X-Axis and Y-Axis, each with a minimum and a maximum, so you can frame a window around whatever the question is about. And More Options, at the bottom of the same menu, switches either axis from Linear to Logarithmic, which is occasionally what you want when one variable runs over several powers of ten.

Desmos usually shows a value as a decimal, like 1.333, while SAT answer choices are usually fractions. The toggle is at the left end of the expression line, the round icon where the color swatch usually sits: click it and the value flips to a fraction. Type 16/12 and the toggle gives back 4/3, so it reduces on the way and what you read is already in lowest terms. It works on coordinates you have clicked too, so an answer you read off the graph can be handed over in whichever form the choices use.

Type an equation with a letter that is not x or y, like y = ax + 1, and Desmos offers to add a slider for a. Click it and that letter becomes a knob: drag, and the graph updates live. This is how you find the value of a constant that makes something true, by watching for it instead of solving for it.

For statistics, type your numbers as a list in square brackets, like L_1 = [3, 5, 8, 12, 18]. Square brackets, not curly braces. Then a function runs on the whole list at once: mean(L_1), median(L_1), stdev(L_1). Type L then 1 and Desmos makes the subscript for you.

For pairs of numbers, x with y, use a table. Type the word table into an empty line and Desmos turns it into two columns, headed x_1 and y_1, with the cursor in the first cell. Type the x-values down the first column and the y-values down the second; every pair plots as a point as you go. The calculator below already has one filled in, so you can see what you are building before you build it.

A filled table shows an Add Regression icon in its left gutter, in the same spot where a plain line has its color swatch. Click it and Desmos fits a line through your points and prints its equation, which is how the regression lesson turns a two-point question into two clicks.