Math Linear functions Calculating the intersection

# Calculating the intersection

The prerequisite for the presence of an intersection is that the two function equations have a different slope.

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### Method

If the condition is met, then calculate the intersection as follows:

1. Equate function equations $X_{ S } \Leftrightarrow f(x)=g(x)$
2. Solve equation for $x$
3. Use $x$ in one of the two equations to calculate $y$

### Example

Calculate the intersection of the two function graphs with the functional equation: $f(x)=1.5x-3$ und $g(x)=-0.25x+4$

1. #### Equate function equations

$f(x)=g(x)$
$1.5x-3=-0.25x+4$
2. #### Solve equation for $x$:

$1.5x-3=-0.25x+4\quad|+3$
$1.5x=-0.25x+7\quad|+0.25x$
$1.75x=7\quad|:1.75x$
$x_{ S }=4$
3. #### Use $x$ in one of the two equations:

$f(x)=1.5x-3$
$f(4)=1.5\cdot4-3$
$y_{ S }=3$
4. #### Intersection:

$S(4|3)$