To find the y-intercept on Desmos, graph the equation, click the curve, and click the gray point on the y-axis. It reads (0, b), and b is the y-intercept. If you prefer numbers to clicking, define the function and type f(0) on a new line, or make a table and read the row where x = 0.
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Question banks: October 2026 Math question bank
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You can try each method 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 page goes deeper than our guide to finding x- and y-intercepts on Desmos: it covers f(0), tables of values, exponential functions and what the y-intercept means in a word problem.
What the y-intercept is
The y-intercept is the value of y when x = 0. On a graph, it is where the line or curve crosses the vertical axis. In slope-intercept form, y = mx + b, it is the b. A function's graph has at most one y-intercept, because a function gives one output for the input 0.
SAT questions use the y-intercept in these ways:
- Direct: what is the y-intercept of this line, curve or function?
- Context: what does the y-intercept represent in a model?
- Comparison: which of two functions has the greater y-intercept?
- Building equations: write the line through two points, or from a table.
Method 1: click the gray point on the y-axis
Desmos's help center says that when you click anywhere on a line or curve, gray dots appear at intercepts, intersection points, maximums and minimums. Click a gray dot to show its coordinates, and click it again to hide them (Desmos Help Center, FAQs).
You just learned the Desmos method. Start with free lesson notes and Targeted Practice, no card needed.
Start 1-day free trial →SAT-style question: What is the y-intercept of the graph of y = 3x - 5?
1 y = 3x - 5- Type the equation on line 1 exactly as written.
- Click the line. Gray dots appear where it crosses each axis.
- Click the gray dot on the y-axis. It reads (0, -5).
- The y-intercept is -5. Check by hand: y = 3(0) - 5 = -5.
The same click works on curves. For the parabola y = x2 - 4x + 3, the gray dot on the y-axis reads (0, 3). In standard form ax2 + bx + c, the constant c is the y-intercept, since every x term is 0 when x = 0.
Method 2: type f(0)
The y-intercept of y = f(x) is f(0). Desmos's Getting Started guide shows this directly: define a function, then type a value such as f(0) on another line (Desmos Help Center, Getting Started). You get a number without hunting for a dot.
SAT-style question: The function f is defined by f(x) = (x - 3)(2x + 5). What is the y-intercept of the graph of y = f(x)?
1 f(x) = (x - 3)(2x + 5)
2 f(0)Line 2 evaluates to -15, so the y-intercept is (0, -15). By hand: (0 - 3)(0 + 5) = -15. Watch the trap here. The numbers 3 and 5 sit in the factors, but neither is the y-intercept. The factors give the x-intercepts, 3 and -5/2.
Method 3: read the x = 0 row of a table
Desmos can build a table from a function. Its Getting Started guide says to press Edit List and then Create Table. By default the table lists inputs from -2 to 2, so the row x = 0 is already there. You can also type other x-values into the table.
Example: Find the y-intercept of y = (2/3)x + 4.
- Type
y = (2/3)x + 4on line 1. - Press Edit List, then Create Table.
- Read the row x = 0. It shows y = 4, so the y-intercept is 4.
Method 4: read it from the equation
When the equation is already in the form y = mx + b, you don't need Desmos. The constant is the y-intercept.
- y = 5x + 3 has a y-intercept of 3.
- y = -2x - 7 has a y-intercept of -7.
- y = x has a y-intercept of 0. The line passes through the origin.
- In standard form, set x = 0. For 4x + 2y = 10, that leaves 2y = 10, so y = 5.
Worked example: y-intercept from two points
SAT-style question: A line passes through the points (2, 7) and (5, 13). What is the y-intercept of the line?
Plotting two points in a table does not draw the line for you. A linear regression does. Desmos's regression guide says to put the data in a table, then type the model on a new line with a tilde (~) in place of the equals sign (Desmos Help Center, Regressions).
1 table x_1 | y_1
2 | 7
5 | 13
2 y_1 ~ m x_1 + b- Add a table and enter the two points as rows.
- On a new line, type
y_1 ~ m x_1 + b. Desmos fits m and b. - The fitted values are m = 2 and b = 3. The y-intercept is 3.
Check by hand: the slope is (13 - 7)/(5 - 2) = 2. Put (2, 7) into y = 2x + b: 7 = 4 + b, so b = 3.
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.
Guided example: a table with no x = 0 row
SAT-style question: The table shows three values of the linear function g. What is the y-intercept of the graph of y = g(x)?
| x | 2 | 4 | 6 |
|---|---|---|---|
| g(x) | 11 | 17 | 23 |
- Each time x goes up by 2, g(x) goes up by 6. The slope is 6/2 = 3.
- Your step: step back from x = 2 to x = 0 and find g(0). Then check it in Desmos with the same table and regression as above.
Check your answer: going from x = 2 to x = 0 subtracts 2 slopes, so g(0) = 11 - 2(3) = 5. The y-intercept is (0, 5), and the regression gives m = 3 and b = 5.
Practice this now: study the free Lines and Linear Relationships lesson notes. The lesson covers intercepts, slope and line equations.
Exponential y-intercepts
For f(x) = a(b)x, the y-intercept is a, because b0 = 1. That makes a the starting amount in growth and decay models. Two variations are easy to misread:
- A constant is added. For f(x) = 4(3)x - 1, f(0) = 4(1) - 1 = 3. The y-intercept is 3, not 4.
- The exponent is shifted. For y = 2x + 3, x = 0 gives 23 = 8. The y-intercept is 8.
Typing f(0) in Desmos handles both cases, so you don't have to decide which number is "the a". If a question gives an exponential table instead of an equation, read our guide to SAT exponential functions from a table 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. Read it as "the amount at the start" or "the part that does not depend on the input".
SAT-style question: A water tank is being drained. The volume V, in liters, left in the tank t minutes after draining begins is V = 900 - 25t. What does 900 represent?
At t = 0, V = 900. So 900 is the volume in the tank when draining begins, and 25 is the number of liters drained per minute. The tank is empty when 25t = 900, at t = 36 minutes. That is the t-intercept, a different question.
SAT-style question: A plumber charges 75 dollars per hour plus a flat service fee. A 3-hour job costs 285 dollars. What is the y-intercept of the cost model, and what does it mean?
Write the cost as C = 75h + b. At h = 3: 285 = 225 + b, so b = 60. The y-intercept is 60: the service fee you pay even if the plumber works 0 hours.
For growth models, the same idea holds. If P(t) = 1,200(1.05)t models a town's population t years after a survey, then P(0) = 1,200 is the population at the time of the survey.
Your turn
Problem 1. The function h is defined by h(x) = 5(0.4)x + 2. What is the y-intercept of the graph of y = h(x)?
Problem 2. The function f is defined by f(x) = 2x + 9. The graph of the linear function g passes through (0, 5) and (3, 11). Which function has the greater y-intercept?
Problem 3. Lines p and q have the same y-intercept. Line p has equation y = 4x + 7. Line q passes through the point (2, 9). What is the slope of line q?
Problem 4. The height H, in centimeters, of a burning candle t hours after it is lit is H = 24 - 1.5t. What does 24 represent?
Answer 1: 7. h(0) = 5(1) + 2 = 7. Type h(0) in Desmos to confirm.
Answer 2: f. Its y-intercept is 9. The point (0, 5) sits on the y-axis, so g has a y-intercept of 5.
Answer 3: 1. Line q also passes through (0, 7), so its slope is (9 - 7)/(2 - 0) = 1.
Answer 4: the height of the candle, 24 centimeters, at the moment it is lit (t = 0).
When Desmos does not show a y-intercept
- Click the curve first. The gray dots appear after you click the line or curve, not the empty grid.
- Bring the point into view. For y = 0.5x + 150, the y-intercept can sit far above your current view. Click Zoom Out, or open Graph Settings and set the y-axis range. You can also define f(x) = 0.5x + 150 and type f(0), which returns 150.
- Check that one exists. A vertical line such as x = 4 never meets the y-axis. The graph of y = 6/x has no y-intercept either, because 6/0 is undefined.
When algebra is faster
College Board's calculator policy notes that some Math questions are better done without a calculator. If the equation is already y = mx + b, read b. If it is a quadratic in standard form, read c. Use Desmos when the function is factored, when it is exponential with a shift, when you only have points or a table, or when you want to check your algebra. For the matching skill on the x-axis, read how to find the x-intercept on Desmos.
Mistakes to avoid
- Reading the coefficient of an exponential. In 4(3)x - 1, the 4 is not the y-intercept. Type f(0) and use the value it returns, 3.
- Reading a number from a factor. In (x - 3)(2x + 5), the 3 and 5 belong to x-intercepts. The y-intercept is the product at x = 0, which is -15.
- Answering with the wrong form. Some questions want the point (0, b) and some want only b. Read the last line of the question before you choose.
Practice next
Work through the lesson notes above, then mix intercept questions with other Math topics in the TTA SAT question bank. For slope and rate of change on the same kind of table, read SAT linear functions on Desmos, 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 articles "FAQs", "Getting Started: Desmos Graphing Calculator" and "Regressions" on September 26, 2026. Every value on this page was recomputed before publishing. The Test Advantage is independent of College Board and Desmos.
Frequently Asked Questions
What is the y-intercept?
It is the point where a graph crosses the y-axis. There x = 0, so the point has the form (0, b). In y = mx + b, the y-intercept is b.
How do I find the y-intercept on Desmos without clicking the graph?
Define the function on one line, for example f(x) = (x - 3)(2x + 5), then type f(0) on the next line. Desmos returns -15, so the y-intercept is (0, -15).
What does the y-intercept mean in a word problem?
It is the starting value: the output when the input is 0. If V = 900 - 25t gives the liters left in a tank t minutes after draining begins, 900 liters is the amount in the tank at the start.
How do I find the y-intercept from two points?
Find the slope, then solve for b. Through (2, 7) and (5, 13), the slope is 2 and 7 = 2(2) + b gives b = 3. On Desmos, put the points in a table and type y_1 ~ m x_1 + b.
What is the y-intercept of an exponential function?
For f(x) = a(b)^x it is a, because b^0 = 1. If a constant is added, include it: f(x) = 4(3)^x - 1 has a y-intercept of 3, not 4.