How to Find the Y-Intercept: From an Equation, a Graph, and a Table

October 20, 2026

The y-intercept is the point where a graph crosses the y-axis. Every point on the y-axis has $x = 0$ , so the y-intercept is always a point of the form

$(0, b) .$

That one fact gives you three ways to find it: from an equation, from a graph, and from a table. Pick whichever one you are handed.

From an equation — set $x = 0$

Replace every $x$ with $0$ and solve for $y$ . The number you get is the height where the graph meets the y-axis.

A line in the form $y = m x + b$ . Take $y = 3 x - 5$ . Set $x = 0$ : $y = 3 \cdot 0 - 5 = - 5$ . The y-intercept is $(0, - 5)$ . In this form the constant term is the answer, because $m \cdot 0$ is always $0$ .

A line in another form. Take $3 x + 2 y = 8$ . Set $x = 0$ : $2 y = 8$ , so $y = 4$ . The y-intercept is $(0, 4)$ . You do not need to rearrange the whole equation first.

A curve. Take $y = x^{2} - 4 x + 7$ . Set $x = 0$ : $y = 0 - 0 + 7 = 7$ . The y-intercept is $(0, 7)$ . The same rule works for any function, not only lines.

A factored curve. Take $y = (x - 2) (x + 3)$ . Set $x = 0$ : $y = (- 2) (3) = - 6$ . The y-intercept is $(0, - 6)$ . Multiply the factors at $x = 0$ ; you do not have to expand.

From a graph — read where it crosses the y-axis

Find the vertical axis. Follow the line or curve until it touches that axis. Read the height of the crossing point. That height is $b$ , and the point is $(0, b)$ .

Green line is y=mx+b. The orange point (0, b) is where it crosses the y-axis. Drag the slider for b to move the point up and down; drag the slider for m to tilt the line and watch the point stay put.

The green line is $y = m x + b$ . Drag the slider for $b$ and the orange point slides up and down the y-axis — the crossing moves with $b$ . Drag the slider for $m$ and the line tilts, but the orange point does not move. Tilting a line changes how steep it is, not where it meets the y-axis. Want more room to try your own line? Open the live board.

If the crossing falls between grid lines, estimate it from the graph, then confirm with the equation by setting $x = 0$ .

Curves cross the y-axis too

A parabola, a wave, or any other function graph meets the y-axis at most once. The rule does not change: look at $x = 0$ .

Green curve is y=ax²+c. The orange point (0, c) is where it crosses the y-axis. Drag the slider for c to move the crossing; drag the slider for a to open or flip the curve while the crossing stays at (0, c).

The green curve is $y = a x^{2} + c$ . Drag the slider for $c$ and the crossing point $(0, c)$ moves with it. Drag the slider for $a$ and the curve opens wider, narrower, or flips upside down, yet it still passes through $(0, c)$ . To keep exploring on a full canvas, open the live board.

From a table — find the row where $x = 0$

If the table has a row with $x = 0$ , you are done: the $y$ value in that row is the y-intercept.

$x$	$y$
$- 1$	$1$
$0$	$4$
$1$	$7$

Here the row $x = 0$ gives $y = 4$ , so the y-intercept is $(0, 4)$ .

No $x = 0$ row? Extrapolate a linear table. Suppose you are given:

$x$	$y$
$2$	$7$
$4$	$11$
$6$	$15$

Check the steps are steady. Each time $x$ goes up by $2$ , $y$ goes up by $4$ . Steady steps mean the points lie on a line.
Find the change per one unit of $x$ : $4 \div 2 = 2$ .
Walk back from $x = 2$ to $x = 0$ . That is two units left, so subtract $2 \cdot 2 = 4$ from $7$ . You get $y = 3$ .

The y-intercept is $(0, 3)$ . Check it: the line is $y = 2 x + 3$ , and at $x = 4$ it gives $11$ , at $x = 6$ it gives $15$ . Both match the table.

Only extrapolate this way when the steps are steady. If the $y$ changes are not constant, the table is not a line, and you need the equation or a graph instead.

When there is no single y-intercept

A vertical line such as $x = 3$ never touches the y-axis, so it has no y-intercept. The vertical line $x = 0$ is the y-axis itself, so it touches it everywhere. Any function has at most one y-intercept, because it gives only one output for the input $x = 0$ . A function with no value at $x = 0$ , such as $y = 1/ x$ , has none.

Two common slips

Setting $y = 0$ instead of $x = 0$ . That finds where the graph crosses the x-axis — a different point.
Writing only the number. The y-intercept of $y = 3 x - 5$ is the point $(0, - 5)$ . Saying " $- 5$ " is fine in conversation, but the point is the full answer.

Where to go next

The handbook section on lines in the plane collects the standard ways of writing a line and where each one meets the axes. For reading any curve as pairs $(x, f (x))$ , see the graph of a real function. For parabolas, where the constant term is the y-axis crossing, see quadratic functions. And if you want to draw the whole graph rather than one point, read how to graph a function.

Equation, graph, or table — the rule is the same every time. Put $x = 0$ and read the height — GoodMaith keeps that point live on the board.