# Beta version

BETA TEST VERSION OF THIS ITEM

This online calculator is currently under heavy development. It may or it may NOT work correctly.

You CAN try to use it. You CAN even get the proper results.

However, please VERIFY all results on your own, as the level of completion of this item is NOT CONFIRMED.

Feel free to send any ideas and comments !

This online calculator is currently under heavy development. It may or it may NOT work correctly.

You CAN try to use it. You CAN even get the proper results.

However, please VERIFY all results on your own, as the level of completion of this item is NOT CONFIRMED.

Feel free to send any ideas and comments !

# Calculations data - line scope and free coefficient

Line scope (a) | ||

Free parameter (b) |

# Results - what we can say about your line

Linear equation formula | Show source$y=2\cdot x+3$ | |

Function zero | Show source$\frac{-3}{2}$ | |

Intersection with the OX axis point | Show source$\left(\frac{-3}{2}, 0 \right)$ | |

Intersection with the OY axis point | Show source$\left(0,3 \right)$ |

# Function graph

# Some facts

- The
**linear function**is a function that can be presented in the following form:

$y= a~ x+ b$where:

**$y$**- function value (the function value at single point x, often marked as f(x)),**$x$**- function argument (called also independent value),**$a$**,**$b$**- linear function coefficients (slope and free parameter).

- The graph of the linear function is
**a straight line**. **Slope**of a linear function defines the degree of slope of the line to the OX axis ("horizontal"). Depending on the slope value, we can distinguish three cases:

- when the slope is zero (a = 0) - the function is reduced to the
**constant function**, its plot is a**line parallel to the OX axis**,

- when the slope is positive (a > 0) - the function is
**increasing**, it's plot is a line going towards the**upper right corner**of the graph,

- when the slope is negative (a < 0) - the function is
**decreasing**, its plot is a line going towards the**lower right corner**of the graph.

- when the slope is zero (a = 0) - the function is reduced to the
- A linear function can have
**one**,**infinitely many**or**no zeros**(roots). This depends on the parameter values **a**and**b**as follow:

- when the slope
**a**is different from zero (a ≠ 0) - the function has**exactly one root**(zero point), the plot of the function**crosses the OX axis one time**in the point:

$x=\frac{- b}{ a}$ - when the slope
**a**is zero, but the free parameter**b**is not (a = 0 and b ≠ 0) - function**has no roots**(zero points), it's plot**does not cross the OX axis**, the function is reduced to the form:

$y = b$ - if both the slope
**a**and the free parameter**b**are zero (a = 0 and b = 0) - the function has**infinite number of roots**(zero points), it's plot**coincides with the axis OX**:

$y = 0$

- when the slope
- The linear function is a
**special case of the polynomial function**with the order of 0 (when a = 0) or 1.

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