Point slope shape
The point slope form or point slope form is a special form of a straight line equation in mathematics . In the point slope form, a straight line is represented in the Euclidean plane with the help of a point on the straight line and the slope of the straight line.
presentation
In the point slope form, a straight line in the plane passing through the point and having the slope is described as the set of those points whose coordinates satisfy the equation
fulfill. If the straight line equation is solved, the explicit representation is obtained
- .
The straight line is then the graph of the function with the function equation
- .
example
In the picture above, for example, the given straight line point and the slope are obtained , and the straight line equation is obtained
respectively
- .
Derivation
Assuming the general shape of a straight line
off, then especially since the point lies on the straight line,
- .
If this equation is solved for and inserted into the general form, it follows
- .
By excluding from one gets the point slope form
- .
conversion
Is using the slope triangle through the point and another straight line point by
calculated, one obtains the two-point form of a straight line equation.
literature
- Frank Paech: Mathematics - clear and entertaining . Carl Hanser Verlag, 2012, ISBN 978-3-446-42874-4 .
- Karl-Heinz Pfeffer: Analysis for technical high schools . Springer, 2010, ISBN 978-3-8348-9646-9 .