To find x- and y-intercepts on Desmos, type the equation and click the graph. Gray points appear where the graph crosses each axis, and clicking a point shows its coordinates. An x-intercept has y = 0, so it looks like (a, 0). A y-intercept has x = 0, so it looks like (0, b).
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Question banks: October 2026 Math question bank
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You can try every step below on the College Board version of Desmos on our Desmos on the SAT page. Bluebook has Desmos built in, and College Board allows a calculator on the entire Math section. This guide covers lines and parabolas, a worked example, practice with answers, and what to do when Desmos is not showing an intercept. If you need only one of the two, read how to find the x-intercept on Desmos or how to find the y-intercept on Desmos.
The rule: set the other variable to 0
- x-intercept: set y = 0 and solve for x. The point is (a, 0).
- y-intercept: set x = 0 and solve for y. The point is (0, b).
The graph of a function has at most one y-intercept. It can have no x-intercepts, one, or several. A parabola has up to two. Before you touch the calculator, read the last line of the question: some ask for the point, and some ask only for the number.
You can graph an intercept in 10 seconds. But can you do it when the clock is ticking? Take a free full Math section and find out.
Start 1-day free trial →How Desmos shows intercepts
Desmos calls these marked spots points of interest. Its help center says they appear in gray when you graph an equation, and you see them after you select the curve, either on the graph or on its expression line. Hover over a gray point to read its coordinates, or select it to keep the label on screen. Desmos also marks the points where two graphs intersect (Desmos Help Center, Getting Started).
That help page describes the standard graphing calculator. Desmos's sheet for the College Board version lists images, folders and notes as the graphing features it turns off. Try the clicks below on the practice calculator before test day so nothing surprises you.
Worked example: the intercepts of a parabola
SAT-style question: In the xy-plane, the graph of y = x2 - 2x - 8 crosses the x-axis at two points and the y-axis at one point. What are the intercepts?
1 y = x^2 - 2x - 8- Type the equation on line 1 exactly as the question gives it. Rearranging first only adds a chance to copy a sign wrong.
- Click the parabola. The gray points show up once the curve is selected.
- Hover over the two gray points on the x-axis. They read (-2, 0) and (4, 0), so the x-intercepts are -2 and 4.
- Hover over the gray point on the y-axis. It reads (0, -8), so the y-intercept is -8.
- If you see any other gray point, skip it. An intercept always has a 0 in one of its coordinates.
Check by hand: x2 - 2x - 8 factors as (x - 4)(x + 2), so y = 0 when x = 4 or x = -2. Setting x = 0 gives y = -8. Both methods agree.
Guided example: a line in standard form
SAT-style question: What are the x-intercept and the y-intercept of the line 4x - 3y = 24?
1 4x - 3y = 24- Find the x-intercept. Set y = 0: 4x = 24, so x = 6. The point is (6, 0).
- Your step: set x = 0 and solve for y.
- Check in Desmos. Type each point on its own line, for example
(6, 0)on line 2. If a point is right, its dot lands on the line.
Check your answer: x = 0 gives -3y = 24, so y = -8. The y-intercept is (0, -8). On line 3, (0, -8) sits on the line, next to the dot for (6, 0).
Clicking the line may also show gray points at both intercepts. The point check works either way, so use it for any equation you type in this form.
See which question types are costing you points
Start with a free mock, free drills, or preview sample questions before using all 45 question banks.
Practice this now: the free Lines and Linear Relationships lesson notes. The lesson covers intercepts, slope and line equations.
Your turn
Problem 1. The function f is defined by f(x) = 2x2 + 5x - 3. The graph of y = f(x) in the xy-plane has x-intercepts at (a, 0) and (b, 0), where a < b. What is the value of b - a?
Problem 2. The function g is defined by g(x) = 3(2)x + 5. What is the y-intercept of the graph of y = g(x), and how many x-intercepts does the graph have?
Answer 1: 7/2, or 3.5. The gray points on the x-axis are (-3, 0) and (0.5, 0), and 0.5 - (-3) = 3.5. By hand, (2x - 1)(x + 3) = 0 gives x = 1/2 or x = -3.
Answer 2: The y-intercept is (0, 8), because g(0) = 3(1) + 5 = 8. The graph has no x-intercepts. 3(2)x is always positive, so g(x) stays above 5 and never reaches 0.
Why Desmos is not showing the x-intercept
If you graph an equation and no gray point appears on the x-axis, run these checks in order.
- Select the graph. Points of interest appear after you select the curve or its expression line. Click on the curve itself, not on empty grid.
- Check that the graph crosses the x-axis. The graph of y = x2 + 4 never goes below 4, so it has no x-intercepts and there is nothing to mark. On the SAT, that tells you x2 + 4 = 0 has no solutions. Problem 2 above works the same way.
- Look outside the window. The x-intercept of y = 0.5x - 40 is at x = 80, which can sit far off to the right of your view. Drag the graph to pan, click Zoom Out, or open Graph Settings and set the x-axis range (Desmos Help Center, Navigate a Graph).
- Check for a touching point. The graph of y = x2 - 6x + 9 touches the x-axis at (3, 0) and turns back up without crossing. Zoom in to see where it touches, then confirm by hand: (x - 3)2 = 0 gives x = 3.
- Still nothing? Type
y = 0on a new line. That line is the x-axis, and Desmos marks the points where two graphs intersect, so click the crossing point. You can also type the point you expect, such as(80, 0), and see whether it lands on the graph.
Intercept or intersection?
An intercept is where one graph meets an axis. An intersection is where two graphs meet each other. The lines y = 2x + 1 and y = -x + 7 intersect at (2, 5), a point that is on neither axis. When a question asks where two graphs cross, you are solving a system; see how to solve systems of equations on Desmos.
What the y-intercept means in a word problem
In a model, the y-intercept is the output when the input is 0. That makes it the starting amount.
SAT-style question: A car rental company charges a flat fee plus a daily rate. The total cost C, in dollars, for d days is C = 45d + 120. What does 120 represent?
At d = 0, C = 120. Before any days are added, the cost is 120 dollars, so 120 is the flat fee and 45 is the cost per day. You can read this one straight from the equation without graphing.
When algebra is faster
College Board's calculator policy notes that some Math questions are better done without a calculator. For y = 3x - 7, the y-intercept is -7 as soon as you read it. For 4x - 3y = 24, covering one variable and dividing takes two short steps. Graph when a quadratic does not factor at a glance, when the equation is long, or when you want to check an answer you found by hand. For more on parabolas, read SAT quadratics on Desmos.
Mistakes to avoid
- Swapping the coordinates. The x-intercept of 4x - 3y = 24 is (6, 0), not (0, 6). Check which axis the gray point sits on before you write it down.
- Copying a rounded decimal. The x-intercept of y = 3x - 1 is 1/3. If the label reads 0.333, match it to the fraction 1/3 before you pick an answer choice.
- Taking an intersection for an intercept. With two graphs on screen, gray points also mark where the graphs meet. Keep only a point with a 0 in it.
Practice next
Work through the lesson notes above until the intercept questions feel routine. Then mix them with other Math topics in the TTA SAT question bank, and keep the Desmos on the SAT guide open for the other calculator techniques.
Checked against College Board's calculator policy and the Desmos Help Center article "Getting Started: Desmos Graphing Calculator" on September 25, 2026. Every intercept on this page was recomputed before publishing. The Test Advantage is independent of College Board and Desmos.
More guides on this skill
Frequently Asked Questions
Why is Desmos not showing the x-intercept?
Click the curve first: Desmos shows its gray points of interest after you select the graph or its expression line. If nothing appears, zoom out, because the intercept may be off screen. Some graphs never cross the x-axis; y = x^2 + 4 has no x-intercepts.
How do you find the y-intercept on Desmos?
Type the equation, click the graph, and hover over the gray point on the y-axis. It reads (0, b), and b is the y-intercept. For y = x^2 - 2x - 8, the point is (0, -8).
What if Desmos gives the intercept as a decimal?
Convert it before you match an answer choice. The x-intercept of y = 3x - 1 is 1/3, so a label of 0.333 means 1/3. Substitute your fraction into the equation to confirm it.
What does the y-intercept mean in a word problem?
It is the starting value, the output when the input is 0. In C = 45d + 120, C = 120 when d = 0, so 120 is the flat fee.
Is an intersection the same as an intercept?
No. An intercept is where one graph meets an axis. An intersection is where two graphs meet, such as (2, 5) for y = 2x + 1 and y = -x + 7.