 # 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, 42000) and (2, 39000)
calculate 8 items:

## Calculate the slope and point-slope form:

 Slope (m)  = y2 - y1 x2 - x1

 Slope (m)  = 39000 - 42000 2 - 1

 Slope (m)  = -3000 1

Slope = -3000

## Calculate the point-slope form :

y - y1 = m(x - x1)
y - 42000 = -3000(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, 42000) and the slope (m) = -3000
b = 42000 - (-3000 * 1)
b = 42000 - 3000
 b  = 45000 1

b = 45000

## Build standard line equation

y = -3000x + 45000

## Distance between the 2 points

D = Square Root((x2 - x1)2 + (y2 - y1)2)
D = Square Root((2 - 1)2 + (39000 - 42000)2)
D = Square Root((12 + -30002))
D = √(1 + 9000000)
D = √9000001
D = 3000.0002

## Midpoint between the 2 points

 Midpoint =
 x2 + x1 2
 ,
 y2 + y1 2
 Midpoint =
 1 + 2 2
 ,
 42000 + 39000 2

 Midpoint =
 3 2
 ,
 81000 2

Midpoint = (3/2, 40500)

## Form a right triangle

Plot a 3rd point (2,39000)
Our first triangle side = 2 - 1 = 1
Our second triangle side = 42000 - 39000 = 3000

Using the slope we calculated
Tan(Angle1) = -3000
Angle1 = Atan(-3000)
Angle1 = -89.9809°
Since we have a right triangle
We only have 90° left
Angle2 = 90 - -89.9809° = 179.9809

## Calculate the y intercept of our line

The y intercept is found by
Setting x = 0 in y = -3000x + 45000
y = -3000(0) + 45000
y = 45000

## 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) = (1,42000) + t(2 - 1,39000 - 42000)
(x,y) = (1,42000) + t(1,-3000)
x = 1 + t
y = 42000 - 3000t

## Calculate Symmetric Equations:

 x - x0 z
 y - y0 b

## Plugging in our numbers, we get:

 x - 1 1
 y - 42000 -3000

## Plot these points on the Cartesian Graph: Slope = -3000/1 or -3000
Slope Intercept = y = -3000x + 45000
Distance Between Points = 3000.0002
Midpoint = (3/2, 40500)
Angle 1 = -89.9809
Angle 2 = 179.9809
Y-intercept = 45000

### 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