 # 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 (-4, 5) and (7, -3)
calculate 8 items:

## Calculate the slope and point-slope form:

 Slope (m)  = y2 - y1 x2 - x1

 Slope (m)  = -3 - 5 7 - -4

 Slope (m)  = -8 11

## Calculate the point-slope form :

y - y1 = m(x - x1)
y - 5 = -8/11(x + 4)

## 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 (-4, 5) and the slope (m) = -8/11
b = 5 - (-8/11 * -4)
b = 5 - (32/11)
 b  = 55 11
 -
 32 11

 b  = 23 11

## Solve for b

This fraction is not reduced. Using our GCF Calculator, we see that the top and bottom of the fraction can be reduced by 23
Our reduced fraction is:
 1 0.478261

## Build standard line equation

y = -8/11x + 1/0.47826086956522

## Distance between the 2 points

D = Square Root((x2 - x1)2 + (y2 - y1)2)
D = Square Root((7 - -4)2 + (-3 - 5)2)
D = Square Root((112 + -82))
D = √(121 + 64)
D = √185
D = 13.6015

## Midpoint between the 2 points

 Midpoint =
 x2 + x1 2
 ,
 y2 + y1 2
 Midpoint =
 -4 + 7 2
 ,
 5 + -3 2

 Midpoint =
 3 2
 ,
 2 2

Midpoint = (3/2, 1)

## Form a right triangle

Plot a 3rd point (7,-3)
Our first triangle side = 7 - -4 = 11
Our second triangle side = 5 - -3 = 8

Using the slope we calculated
Tan(Angle1) = -0.72727272727273
Angle1 = Atan(-0.72727272727273)
Angle1 = -36.0274°
Since we have a right triangle
We only have 90° left
Angle2 = 90 - -36.0274° = 126.0274

## Calculate the y intercept of our line

The y intercept is found by
Setting x = 0 in y = -8/11x + 1/0.47826086956522
y = -8/11(0) + 1/0.47826086956522
y = 1/0.47826086956522

## 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) = (-4,5) + t(7 - -4,-3 - 5)
(x,y) = (-4,5) + t(11,-8)
x = -4 + 11t
y = 5 - 8t

## Calculate Symmetric Equations:

 x - x0 z
 y - y0 b

## Plugging in our numbers, we get:

 x - -4 11
 y - 5 -8

## Plot these points on the Cartesian Graph:   Slope = -8/11 or -0.72727272727273
Slope Intercept = y = -8/11x + 1/0.47826086956522
Distance Between Points = 13.6015
Midpoint = (3/2, 1)
Angle 1 = -36.0274
Angle 2 = 126.0274
Y-intercept = 1/0.47826086956522

### 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