Linear function calculator
Calculator helpful during common operations related to linear function such as calculating value at given point or finding out zero of a function (root).

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.
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Calculations data - enter values, that you know here

Function value (yy)
(the function value at single point x, often marked as f(x))
=>
Slope (aa)
(number that describes the direction and the steepness of the line, sometimes is called gradient)
<=
Zero of the function (xx)
(argument for which the function has a value of zero, its a solution of f(x) = 0 equation)
=>
Function argument (xx)
<=
Free parameter (bb)
<=
X coordinate of the point (x0x_0)
=>
Y coordinate of the point (y0y_0)
=>
X coordinate of the first point (x0x_0)
=>
Y coordinate of the first point (y0y_0)
=>
X coordinate of the second point (x1x_1)
=>
Y coordinate of the second point (y1y_1)
=>

Result: function value (yy)

Summary
Used formulaShow sourcey=a x+b y= a~ x+ b
ResultShow source22
Numerical resultShow source22
Result step by step
1Show source11+11\cdot1+1Multiply by one
2Show source1+11+1Simplify arithmetic
3Show source22Result
Numerical result step by step
1Show source22Result

Some facts

  • The linear function is a function that can be presented in the following form:
    y=a x+b y= a~ x+ b
    where:
    • yy - function value (the function value at single point x, often marked as f(x)),
    • xx - function argument (called also independent value),
    • aa, bb - 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=ba 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 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=0y = 0
  • 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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