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

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Given (1, 3) and (0, 0)

calculate 8 items:

Calculate the slope and point-slope form:

Slope (m) =	y2 - y1
	x2 - x1

Slope (m) =	0 - 3
	0 - 1

Slope (m) =	-3
	-1

Slope = 3

Calculate the point-slope form :

y - y1 = m(x - x1)

y - 3 = 3(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, 3) and the slope (m) = 3

b = 3 - (3 * 1)

b = 3 + 0

b =	3
	1

Solve for b

b = -3/-1

Build standard line equation

y = 3x

Distance between the 2 points

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

D = Square Root((0 - 1)2 + (0 - 3)2)

D = Square Root((-12 + -32))

D = √(1 + 9)

D = √10

D = 3.1623

Midpoint between the 2 points

Midpoint =

Midpoint =

Midpoint =

Form a right triangle

Plot a 3rd point (1,0)

Our first triangle side = 1 - 0 = 1

Our second triangle side = 3 - 0 = 3

Using the slope we calculated
Tan(Angle1) = 3

Angle1 = Atan(3)

Angle1 = 71.5651°

Since we have a right triangle
We only have 90° left
Angle2 = 90 - 71.5651° = 18.4349

Calculate the y intercept of our line

The y intercept is found by
Setting x = 0 in y = 3x

y = 3(0)

y =

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) = (1,3) + t(0 - 1,0 - 3)

(x,y) = (1,3) + t(-1,-3)

x = 1 - t

y = 3 - 3t

Calculate Symmetric Equations:

Plugging in our numbers, we get:

Plot these points on the Cartesian Graph:

Final Answers

Slope = 0/-1 or 3
Slope Intercept = y = 3x
Distance Between Points = 3.1623
Midpoint = (1/2, 3/2)
Angle 1 = 71.5651
Angle 2 = 18.4349
Y-intercept =

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What is the Answer?

Slope = 0/-1 or 3
Slope Intercept = y = 3x
Distance Between Points = 3.1623
Midpoint = (1/2, 3/2)
Angle 1 = 71.5651
Angle 2 = 18.4349
Y-intercept =

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?

anglethe figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. distanceinterval between two points in time
d = rtline equationparametric equationdefines a group of quantities as functions of one or more independent variables called parameters.point slope formshow 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)slopeChange in y over change in xsymmetric equationsan 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 planey-interceptA point on the graph crossing the y-axis

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