Given (6, 2) and (9, 6)
calculate 8 items:
Calculate the slope and point-slope form:
| Slope (m) = | y2 - y1 |
| x2 - x1 |
| Slope (m) = | 6 - 2 |
| 9 - 6 |
| Slope (m) = | 4 |
| 3 |
Calculate the point-slope form :
y - y1 = m(x - x1)
y - 2 = 4/3(x - 6)
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 (6, 2) and the slope (m) = 4/3
b = 2 - (4/3 * 6)
b = 2 - (24/3)
| b = | 6 |
| 3 |
| - |
| 24 |
| 3 |
| b = | -18 |
| 3 |
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 18
Our reduced fraction is:
| 1 | |
| 0.16666666666667 |
Build standard line equation
y = 4/3x - 6
Distance between the 2 points
D = Square Root((x2 - x1)2 + (y2 - y1)2)
D = Square Root((9 - 6)2 + (6 - 2)2)
D = Square Root((32 + 42))
D = √(9 + 16)
D = √25
D = 5
Midpoint between the 2 points
| Midpoint = |
| x2 + x1 |
| 2 |
| , |
| y2 + y1 |
| 2 |
| Midpoint = | |
| 6 + 9 |
| 2 |
| , |
| 2 + 6 |
| 2 |
| Midpoint = | |
| 15 |
| 2 |
| , |
| 8 |
| 2 |
Midpoint = (15/2, 4)
Form a right triangle
Plot a 3rd point (9,2)
Our first triangle side = 9 - 6 = 3
Our second triangle side = 6 - 2 = 4
Using the slope we calculated
Tan(Angle1) = 1.3333333333333
Angle1 = Atan(1.3333333333333)
Angle1 = 53.1301°
Since we have a right triangle
We only have 90° left
Angle2 = 90 - 53.1301° = 36.8699
Calculate the y intercept of our line
The y intercept is found by
Setting x = 0 in y = 4/3x - 6
y = 4/3(0) - 6
y = -6
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) = (6,2) + t(9 - 6,6 - 2)
(x,y) = (6,2) + t(3,4)
x = 6 + 3t
y = 2 + 4t
Calculate Symmetric Equations:
| x - x0 | |
| z |
| y - y0 |
| b |
Plugging in our numbers, we get:
| x - 6 | |
| 3 |
| y - 2 |
| 4 |
Plot these points on the Cartesian Graph:
Final Answers
Slope Intercept = y = 4/3x - 6
Distance Between Points = 5
Midpoint = (15/2, 4)
Angle 1 = 53.1301
Angle 2 = 36.8699
Y-intercept = -6
You have 2 free calculationss remaining
What is the Answer?
Slope Intercept = y = 4/3x - 6
Distance Between Points = 5
Midpoint = (15/2, 4)
Angle 1 = 53.1301
Angle 2 = 36.8699
Y-intercept = -6
How does the Line Equation-Slope-Distance-Midpoint-Y intercept Calculator work?
* 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?
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
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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