Y Intercept Calculator

Four boxes, one line. Type the two points your line passes through, click Calculate, and this y intercept calculator answers at once.

• First point: x (x₁) - the x-coordinate of your first point, such as 2
• First point: y (y₁) - the matching y-value, such as 3
• Second point: x (x₂) - the second point's x, such as 4
• Second point: y (y₂) - the matching y-value, such as 7

Two points fix one line, and the y intercept calculator sends back three rows:

• Check reads true when the two x-values differ. False means both points share one x: a vertical line, no intercept.
• Slope (m) is the rise over run between your points - the y intercept calculator's first formula.
• y-intercept (b) is where the line crosses the y-axis - the y intercept calculator's headline answer.

Have the equation instead of two points? A second group of three boxes reads it directly.

• Standard form: a, b, c carry the equation a·x + b·y = c, such as 3, 2, 12 for 3x + 2y = 12.
• Fill whichever group you have. The y intercept calculator runs the rows for the complete one.
• Slope from standard form (m) returns -a/b; y-intercept from standard form returns c/b - the equation-side rows of the y intercept calculator.

Join m and b into y = m\cdot x + b. The sample values return m = 2 and b = -1 from the y intercept calculator: the line y = 2x - 1.

This page is more than a static y intercept calculator - it is also an AI tutor:

• Ask in plain words. "My line goes through (1, 5) and (3, 9) - where does it cut the y-axis?" The AI fills the boxes and runs the y intercept calculator for you.
• Take a photo of your homework. The AI reads the points and fills the y intercept calculator form.
• Ask about the ideas. "Why does b come out negative?" The AI explains step by step - every number still comes from the calculator on this page.
• Work backwards, then keep asking. Give a slope and one point, or an equation. The AI shows the route, and the y intercept calculator keeps answering.

The y-intercept is the point where a line crosses the y-axis - the spot a y intercept calculator reports as a number. Its x is always 0, so it is written (0, b); the y intercept finder above hunts for exactly that point.

The picture shows the whole job the y intercept calculator does. A line climbs through (2, 3) and (4, 7); rise 4, run 2, so m = 2. Slide back along the line to x = 0 and you land on (0, -1): the intercept b.

An intercept is also a starting value - the fee before any miles, the cost before any pizzas. Example 2 reads it that way. Type (2, 3) and (4, 7) into the y intercept calculator above: back come m = 2 and b = -1.

Graph for slope and y intercept

Reading the graph for slope and y intercept together is the fastest check there is. The tilt gives m and the y-axis crossing gives b; the y intercept calculator agrees with both once you type the points.

Symbols now - the same four boxes from the form. The slope and y intercept calculator runs two short formulas:

$m = \dfrac{y_2 - y_1}{x_2 - x_1}$

$b = y_1 - m \cdot x_1$

One line then holds everything: $y = mx + b$. This y intercept calculator section maps your data to a route:

Every route ends in the same two numbers. That is all a slope and y intercept calculator computes - and the y intercept calculator above skips the algebra.

Holding an equation instead? A y mx b calculator saves the slope work. Solve for y and the letters do the rest: the x coefficient is m, the constant at the end is b. That is why the y intercept calculator form carries that name.

Take $y = \frac{1}{2}x + 3$: slope \frac{1}{2}, intercept (0, 3), no arithmetic - and the y intercept calculator returns the same pair from (0, 3) and (2, 4). Not solved for y? Set x = 0 and see which y remains - same fact, different clothes.

Homework equations arrive in standard form, so the y mx b calculator route needs that solve-for-y step first. Example 2 runs it; the y intercept calculator then confirms b from two points of the line.

British textbooks say gradient for slope and often write y = mx + c. Different letters, identical mathematics - c still marks the intercept, and the y intercept calculator on this page would find it just the same. A gradient intercept calculator is simply this page in UK spelling: same boxes, same two rows.

If your class writes y = mx + c, read every b here as c. The y intercept calculator never cares about spelling - slope finder, slope formula calculator, gradient intercept calculator, y mx b calculator: the boxes answer all.

Give the y intercept calculator its home data: a line leaves you (2, 3) and (4, 7). Find the slope, the intercept, and the line.

1. Slope: $m = \dfrac{7 - 3}{4 - 2} = \dfrac{4}{2} = 2$.
2. Intercept: $b = y_1 - m \cdot x_1 = 3 - 2 \cdot 2 = -1$.
3. Full line: $y = 2x - 1$, crossing the y-axis at $(0, -1)$.

Check with the other point: $2 \cdot 4 - 1 = 7$, exactly the $y_2$ you typed. Feed 2, 3, 4, 7 to the y intercept calculator above - both rows agree instantly.

Equations arrive in standard form. Take 3x + 2y = 12: where does its line cross the y-axis? The y intercept calculator eats points, not equations, so run the set-x-to-0 route.

1. Set x = 0, because the y-axis lives at x = 0: $2y = 12$.
2. Solve: $y = 6$, so the intercept is $(0, 6)$.
3. Read-off check: solved for y, the equation is $y = -\dfrac{3}{2}x + 6$ - constant 6, slope $-\dfrac{3}{2}$.

Two points of this line, like (0, 6) and (2, 3), also feed the y intercept calculator directly. So does the equation itself: type 3, 2, 12 into the standard-form boxes of this y intercept calculator and both rows appear.

Now reverse the flow - the direction no static y intercept calculator advertises. A line has slope 2 and passes through (4, 7). Where does it cross the y-axis?

1. The formula runs on any point of the line: $b = y - m \cdot x$.
2. Substitute: $b = 7 - 2 \cdot 4 = -1$.
3. Crossing point $(0, -1)$, line $y = 2x - 1$ - Example 1 backwards.

Given b = -1 and m = 2, any point follows: at x = 4, $y = 2 \cdot 4 - 1 = 7$. Tests love all three directions; the y intercept calculator answers the two-point one.

Three slips the y intercept calculator catches daily:

1. Flipping the slope fraction. Rise goes on top: $m = \dfrac{y_2 - y_1}{x_2 - x_1}$. Flip it and the y intercept calculator reports m = 0.5 instead of 2 - every later number dies.
2. Mixing the points' coordinates. Each x travels with its own y. Pair x from one point with y from the other and you build a line through neither - the y intercept calculator never mixes its four boxes.
3. Skipping the vertical check. Same x on both points means a vertical line: undefined slope, no y-intercept. The Check row of the y intercept calculator exists for this.