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 $y=mx+n$

$y=0.5x+5$