## Enter 2 points 1 point and the slope

Point 1:
(x1 = , y1 = )   Slope:
Point 2:
(x2 = , y2 = )    b:

Given (3, 22) and (4, 24)

calculate 8 items:

##### Calculate the slope and point-slope form:

 Slope (m)  = y2 - y1 x2 - x1

 Slope (m)  = 24 - 22 4 - 3

 Slope (m)  = 2 1

Slope = 2

##### Calculate the point-slope form :

y - y1 = m(x - x1)

y - 22 = 2(x - 3)

##### 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 (3, 22) and the slope (m) = 2

b = 22 - (2 * 3)

b = 22 + 6

 b  = 16 1

b = 16

y = 2x + 16

##### Distance between the 2 points

D = Square Root((x2 - x1)2 + (y2 - y1)2)

D = Square Root((4 - 3)2 + (24 - 22)2)

D = Square Root((12 + 22))

D = √(1 + 4)

D = √5

D = 2.2361

##### Midpoint between the 2 points

 Midpoint =
 x2 + x1 2
 ,
 y2 + y1 2
 Midpoint =
 3 + 4 2
 ,
 22 + 24 2

 Midpoint =
 7 2
 ,
 46 2

Midpoint = (7/2, 23)

##### Form a right triangle

Plot a 3rd point (4,22)

Our first triangle side = 4 - 3 = 1

Our second triangle side = 24 - 22 = 2

Using the slope we calculated
Tan(Angle1) = 2

Angle1 = Atan(2)

Angle1 = 63.4349°

Since we have a right triangle
We only have 90° left
Angle2 = 90 - 63.4349° = 26.5651

##### Calculate the y intercept of our line

The y intercept is found by
Setting x = 0 in y = 2x + 16

y = 2(0) + 16

y = 16

##### 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) = (3,22) + t(4 - 3,24 - 22)

(x,y) = (3,22) + t(1,2)

x = 3 + t

y = 22 + 2t

##### Calculate Symmetric Equations:

 x - x0 z
 y - y0 b

##### Plugging in our numbers, we get:

 x - 3 1
 y - 22 2

##### Plot these points on the Cartesian Graph:

Slope = 2/1 or 2
Slope Intercept = y = 2x + 16
Distance Between Points = 2.2361
Midpoint = (7/2, 23)
Angle 1 = 63.4349
Angle 2 = 26.5651
Y-intercept = 16

Slope = 2/1 or 2
Slope Intercept = y = 2x + 16
Distance Between Points = 2.2361
Midpoint = (7/2, 23)
Angle 1 = 63.4349
Angle 2 = 26.5651
Y-intercept = 16
##### 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