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

21 May 2024, 00:00

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

Solve for b

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 =

Midpoint =

42000 + 39000

Midpoint =

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:

Plugging in our numbers, we get:

y - 42000

-3000

Plot these points on the Cartesian Graph:

Final Answers

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

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What is the Answer?

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?

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

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

Given (1, 42000) and (2, 39000) calculate 8 items: Slope = -3000 y - y1 = m(x - x1) y - 42000 = -3000(x - 1) Standard equation of a line is y = mx + bwhere m is our slopex and y are points on the lineb is a constant.