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.

Y-Intercept - dCode

Tag(s) : Geometry, Functions

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⮞ Go to: X-Intercept

⮞ Go to: Slope Coefficient

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

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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Cite as source (bibliography):

*Y-Intercept* on dCode.fr [online website], retrieved on 2024-07-18,

intercept,y,axis,line,linear,equation,coefficient,slope,abcissa,affine,function

https://www.dcode.fr/y-intercept

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