Analytic geometry: straight line calculator
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
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

# Calculations data - line scope and free coefficient#

 Line scope (a) Free parameter (b)

 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$\left(0,3 \right)$

# 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.

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