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Y-Intercept

Tool for calculating the y-intercept of a line from 2 points or from 1 point and the slope coefficient. Calculation of the intercept of the line with the y-axis.

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Y-Intercept -

Tag(s) : Geometry, Functions

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# Y-Intercept

## X-Intercept Calculator

⮞ Go to: X-Intercept

## Slope coefficient calculator

### What is the y-intercept? (Definition)

The y-intercept is the intersection point of the function/line with the y (ordinate) axis for the abscissa value x = 0 (origin).

### How to calculate the y intercept?

The general formula for finding the y-intercept of a function $y = f(x)$ is to calculate the value of $y$ when $x = 0$.

From the function expression

For any function (not necessarily affine/linear), calculate the value for $x = 0$. The value obtained is the y-intercept.

Example: A curve of equation $y = 3x^2 + 1$, with $x = 0$ is $y = 3 \times 0^2 + 1 = 1$, so $1$ is the y-intercept

For an equation of a line of the plane, the equation has the form $a x + b$ with $b$ the y-intercept.

Example: A line of equation y=3x+4 has 4 as y-intercept

From 2 points (line only)

With 2 points, can be calculated the equation of the line (see the linear equation calculator) and thus to deduce the y-intercept (see above)

From the slope coefficient and 1 point (line only)

Knowing the slope coefficient of a line and a point, can be deduced from the equation of the line (see the linear equation calculation) and thus deduce the y-intercept (see above).

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Y-Intercept on dCode.fr [online website], retrieved on 2022-12-09, https://www.dcode.fr/y-intercept

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