Given (0, 20) and (12, 30)
calculate 8 items:
Calculate the slope and point-slope form:
| Slope (m)= | y2 - y1 |
| x2 - x1 |
| Slope (m)= | 30 - 20 |
| 12 - 0 |
| Slope (m)= | 10 |
| 12 |
GCF Calculation
Reduce numerator and denominator by the (GCF) of 10
Slope = (10/10)/(12/10)
| Slope= | 1 |
| 1.2 |
Calculate the point-slope form :
y - y1 = m(x - x1)
y - 20 = 5/6(x - 0)
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 (0, 20) and the slope (m) = 5/6
b = 20 - (5/6 * 0)
b = 20 - (0/1.2)
| b= | 24 |
| 1.2 |
| b= | 120 |
| 6 |
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 120
Our reduced fraction is:
Build standard line equation
y = 5/6x + 20
Distance between the 2 points
D = Square Root((x2 - x1)2 + (y2 - y1)2)
D = Square Root((12 - 0)2 + (30 - 20)2)
D = Square Root((122 + 102))
D = √(144 + 100)
D = √244
D = 15.6205
Midpoint between the 2 points
| Midpoint = |
| Midpoint = | |
| Midpoint = | |
Midpoint = (6, 25)
Form a right triangle
Plot a 3rd point (12,20)
Our first triangle side = 12 - 0 = 12
Our second triangle side = 30 - 20 = 10
Using the slope we calculated
Tan(Angle1) = 0.83333333333333
Angle1 = Atan(0.83333333333333)
Angle1 = 39.8056°
Since we have a right triangle
We only have 90° left
Angle2 = 90 - 39.8056° = 50.1944
Calculate the y intercept of our line
The y intercept is found by
Setting x = 0 in y = 5/6x + 20
y = 5/6(0) + 20
y = 20
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) = (0,20) + t(12 - 0,30 - 20)
(x,y) = (0,20) + t(12,10)
x = 0 + 12t
y = 20 + 10t
Calculate Symmetric Equations:
Plugging in our numbers, we get:
Plot these points on the Cartesian Graph:
Final Answers
Slope = 1/1.2 or 0.83333333333333
Slope Intercept = y = 5/6x + 20
Distance Between Points = 15.6205
Midpoint = (6, 25)
Angle 1 = 39.8056
Angle 2 = 50.1944
Y-intercept = 20
You have 1 free calculations remaining
What is the Answer?
Slope = 1/1.2 or 0.83333333333333
Slope Intercept = y = 5/6x + 20
Distance Between Points = 15.6205
Midpoint = (6, 25)
Angle 1 = 39.8056
Angle 2 = 50.1944
Y-intercept = 20
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
Line Equation-Slope-Distance-Midpoint-Y intercept Calculator Video
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