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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:
   
Given (1, 4) and (5, 6)
calculate 8 items:

Calculate the slope and point-slope form:
Slope (m)  =  y2 - y1
  x2 - x1

Slope (m)  =  6 - 4
  5 - 1

Slope (m)  =  2
  4

Since the slope is not fully reduced, we reduce numerator and denominator by the (GCF) of 2
Slope = (2/2)/(4/2)
Slope = 1/2

Calculate the point-slope form :

y - y1 = m(x - x1)
y - 4 = 1/2(x - 1)

Calculate the line equation
Standard equation of a line is y = mx + b
where m is our slope
x and y are points on the line
b is a constant.

Rearrange the equation to solve for b
we get b = y - mx.
Use (1, 4) and the slope (m) = 1/2
b = 4 - (1/2 * 1)
b = 4 - (1/2)
b  =  8
  2
-
  
1
2
b  =  7
  2

This fraction is not reduced. Using our GCF Calculator, we see that the top and bottom of the fraction can be reduced by 7
Our reduced fraction is:
1
0.28571428571429

Build standard line equation

y = 1/2x + 1/0.28571428571429

Distance between the 2 points
D = Square Root((x2 - x1)2 + (y2 - y1)2)
D = Square Root((5 - 1)2 + (6 - 4)2)
D = Square Root((42 + 22))
D = √(16 + 4)
D = √20
D = 4.4721

Midpoint between the 2 points
Midpoint =
  
x2 + x1
2
  
,
y2 + y1
2
Midpoint =
  
1 + 5
2
  
,
4 + 6
2

Midpoint =
  
6
2
  
,
10
2

Midpoint = (3, 5)

Form a right triangle
Plot a 3rd point (5,4)
Our first triangle side = 5 - 1 = 4
Our second triangle side = 6 - 4 = 2

Using the slope we calculated
Tan(Angle1) = 0.5
Angle1 = Atan(0.5)
Angle1 = 26.5651°
Since we have a right triangle
We only have 90° left
Angle2 = 90 - 26.5651° = 63.4349

Calculate the y intercept of our line

The y intercept is found by
Setting x = 0 in y = 1/2x + 1/0.28571428571429
y = 1/2(0) + 1/0.28571428571429
y = 1/0.28571428571429

Find the parametric equations for the line

Parametric equations are written as
(x,y) = (x0,y0) + t(b,-a)

Plugging in our numbers, we get

(x,y) = (1,4) + t(5 - 1,6 - 4)
(x,y) = (1,4) + t(4,2)
x = 1 + 4t
y = 4 + 2t

Calculate Symmetric Equations:

x - x0
z
  
y - y0
b

Plugging in our numbers, we get:

x - 1
4
  
y - 4
2

Plot these points on the Cartesian Graph:


ANSWERS:
<-- Slope
<-- Slope Intercept Form Line Equation
<-- Distance between points
<-- Midpoint
<-- Angle 1
<-- Angle 2
<-- Y intercept

What is the Answer?

Slope (m) = 1/2 or 0.5

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?

  1. m = (y2 - y1) / (x2 - x1)
  2. y = mx + b
  3. Distance = Square Root((x2 - x1)2 + (y2 - y1)2)
  4. Parametric equations are written in the form (x,y) = (x0,y0) + t(b,-a)
  5. 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

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


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