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#

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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

What do you want to calculate today?#

Choose a scenario that best fits your needs

I know function argument (

x

) and linear function coefficients (

a

b

) and want to calculate function value (

y

)I know function argument (

x

), slope (

a

) and point coordinates (

x_0

y_0

) and want to calculate function value (

y

)I know coordinates of the first point (

x_0

y_0

) and coordinates of the second point (

x_1

y_1

) and want to calculate slope (

a

)I know free parameter (

b

) and point coordinates (

x_0

y_0

) and want to calculate slope (

a

)I know free parameter (

b

) and zero of the function (

x

) and want to calculate slope (

a

)I know slope (

a

) and point coordinates (

x_0

y_0

) and want to calculate zero of the function (

x

)I know coordinates of the first point (

x_0

y_0

) and coordinates of the second point (

x_1

y_1

) and want to calculate zero of the function (

x

)

Calculations data - enter values, that you know here#

Function value ( $y$ ) (the function value at single point x, often marked as f(x))		=>
Slope ( $a$ ) (number that describes the direction and the steepness of the line, sometimes is called gradient)		<=
Zero of the function ( $x$ ) (argument for which the function has a value of zero, its a solution of f(x) = 0 equation)		=>
Function argument ( $x$ )		<=
Free parameter ( $b$ )		<=
X coordinate of the point ( $x_0$ )		=>
Y coordinate of the point ( $y_0$ )		=>
X coordinate of the first point ( $x_0$ )		=>
Y coordinate of the first point ( $y_0$ )		=>
X coordinate of the second point ( $x_1$ )		=>
Y coordinate of the second point ( $y_1$ )		=>

Result: function value ( $y$ )#

Summary

Used formula

Show source

y=a \cdot x+b

Result

Show source

2

Numerical result

Show source

2

Result step by step

1	Show source $1 \cdot 1+1$	Multiply by one	Any number multiplied by one (1) gives the same number: $a \cdot 1 = 1 \cdot a = a$
2	Show source $1+1$	Simplify arithmetic	-
3	Show source $2$	Result	Your expression reduced to the simplest form known to us.

Numerical result step by step

1	Show source $2$	The original expression	-
2	Show source $2$	Result	Your expression reduced to the simplest form known to us.

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.