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

Publish date: 2024-07-15

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

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
0.47826086956522

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 =

Midpoint =

Midpoint =

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:

Plugging in our numbers, we get:

Plot these points on the Cartesian Graph:

Final Answers

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

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What is the Answer?

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