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:


    $S(4|3)$