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.
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 !

# 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 formulaShow source$y= a~ x+ b$
ResultShow source$2$
Numerical resultShow source$2$
Result step by step
 1 Show source$1\cdot1+1$ Multiply by one 2 Show source$1+1$ Simplify arithmetic 3 Show source$2$ Result
Numerical result step by step
 1 Show source$2$ Result

# 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.
• 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.

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