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Line Equation-Slope-Distance-Midpoint-Y intercept Calculator

Enter 2 points 1 point and the slope

Point 1:
(x1 = , y1 = )   Slope: Point 2:
(x2 = , y2 = )    b:
   
With a slope of 4
A point (x1, y1) = (3, 2):
Calculate the point-slope form.

The standard line equation is y = mx + b

Rearrange that equation to solve for b
we get b = y - mx.

Plug in our known values

b = 2 - (4 * 3)
b = 2 - 12
b = -10

Calculate the y intercept

The y intercept is found by
Setting x = 0 in y = 4x - 10
y = 4(0) - 10
y = -10

Calculate the point-slope form:

y - y1 = m(x - x1)
y - 2 = 4(x - 3)

Build our standard line equation




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What is the Answer?

y = 4x - 10

How does the Line Equation-Slope-Distance-Midpoint-Y intercept Calculator work?

Free Line Equation-Slope-Distance-Midpoint-Y intercept Calculator - Enter 2 points, and this calculates the following:
* Slope of the line (rise over run) and the line equation y = mx + b that joins the 2 points
* Midpoint of the two points
* Distance between the 2 points
* 2 remaining angles of the rignt triangle formed by the 2 points
* y intercept of the line equation
* Point-Slope Form
* Parametric Equations and Symmetric Equations

Or, if you are given a point on a line and the slope of the line including that point, this calculates the equation of that line and the y intercept of that line equation, and point-slope form.

Also allows for the entry of m and b to form the line equation
This calculator has 7 inputs.

What 6 formulas are used for the Line Equation-Slope-Distance-Midpoint-Y intercept Calculator?

m = (y2 - y1) / (x2 - x1)
y = mx + b
Distance = Square Root((x2 - x1)2 + (y2 - y1)2)
Parametric equations are written in the form (x,y) = (x0,y0) + t(b,-a)
Midpoint = ((x2 + x1)/2, (y2 + y1)/2)


For more math formulas, check out our Formula Dossier

What 9 concepts are covered in the Line Equation-Slope-Distance-Midpoint-Y intercept Calculator?

angle
the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
distance
interval between two points in time
d = rt
line equation
parametric equation
defines a group of quantities as functions of one or more independent variables called parameters.
point slope form
show you how to find the equation of a line from a point on that line and the line's slope.
y - y1 = m(x - x1)
slope
Change in y over change in x
symmetric equations
an equation that presents the two variables x and y in relationship to the x-intercept a and the y-intercept b of this line represented in a Cartesian plane
y-intercept
A point on the graph crossing the y-axis

Example calculations for the Line Equation-Slope-Distance-Midpoint-Y intercept Calculator

  1. (1,4)(2,6)
  2. (-4,5) and (7,-3)
  3. (3,2);m=4
  4. m=4,b=-3

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