Enter parameters of your line (scope and free parameter) and check out what we can say about it such as zero point, function graph etc.

Beta version#

BETA TEST VERSION OF THIS ITEM
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Symbolic algebra

ⓘ Hint: This calculator supports symbolic math. You can enter numbers, but also symbols like a, b, pi or even whole math expressions such as (a+b)/2. If you still don't sure how to make your life easier using symbolic algebra check out our another page: Symbolic calculations

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 $y=2~x+3$
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:

$y=a \cdot x+b$
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.
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:
  
  $y = 0$
The linear function is a special case of the polynomial function with the order of 0 (when a = 0) or 1.

Tags and links to this website#

Tags:

line · straight_line · line_graph · line_equation

Tags to Polish version:

prosta · linia_prosta · wykres_prostej · rownanie_prostej

What tags this calculator has#

CALCULATOR · MATH · A -> Z (all)

Permalink#

This is permalink. Permalink is the link containing your input data. Just copy it and share your work with friends:

https://calculla.com/line?inLineScope=$symbolic(2)&inFreeParameter=$symbolic(3)

Links to external sites (leaving Calculla?)#