Math ↠ Linear functions ↠ Determine the y-intercept

Determine the y-intercept n

The y-intercept (ordinate intercept) $n$ can be calculated using the slope $m$ and a point $P_{ 1 }(x_{ 1 }|y_{ 1 })$ by inserting it into the general equation and converting it:

$y_{ 1 }=m\cdot x_{ 1 }+n$
$n=y_{ 1 }-m\cdot x_{ 1 }$
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Tip

Mostly it is possible to read the y-intercept from the line at point $P(0|n)$. For this, read off the$y$-value at the position $x = 0$.

Example


  1. Read 2 points, e.g.


    $P_{ 1 }(2|6)$ und $P_{ 2 }(6|8)$

  2. Calculate slope


    $m=\frac{ \Delta y }{ \Delta x }=\frac{ y_{ 2 } - y_{ 1 } }{ x_{ 2 }-x_{ 1 } }=\frac{ 8-6 }{ 6-2 }=\frac{ 2 }{ 4 }=0.5$

  3. Insert slope $m=0.5$ and $P_{ 1 }(2|6)$ into the equation


    $n=y_{ 1 }-m\cdot x_{ 1 }=6-0.5\cdot 2=5$

  4. Insert y-intercept $n=5$ und slope $m=0.5$ in $y=mx+n$


    $y=0.5x+5$