Given (10, -2) and (4, 4)
calculate 8 items:
Calculate the slope and point-slope form:
| Slope (m) = | y2 - y1 |
| x2 - x1 |
| Slope (m) = | 4 - -2 |
| 4 - 10 |
| Slope (m) = | 6 |
| -6 |
Slope = -1
Calculate the point-slope form :
y - y1 = m(x - x1)
y - -2 = -1(x - 10)
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 (10, -2) and the slope (m) = -1
b = -2 - (-1 * 10)
b = -2 + 10
| b = | 8 |
| 1 |
Solve for b
b = -8/-1
Build standard line equation
y = -x + 8
Distance between the 2 points
D = Square Root((x2 - x1)2 + (y2 - y1)2)
D = Square Root((4 - 10)2 + (4 - -2)2)
D = Square Root((-62 + 62))
D = √(36 + 36)
D = √72
D = 8.4853
Midpoint between the 2 points
| Midpoint = |
| x2 + x1 |
| 2 |
| , |
| y2 + y1 |
| 2 |
| Midpoint = | |
| 10 + 4 |
| 2 |
| , |
| -2 + 4 |
| 2 |
| Midpoint = | |
| 14 |
| 2 |
| , |
| 2 |
| 2 |
Midpoint = (7, 1)
Form a right triangle
Plot a 3rd point (10,-2)
Our first triangle side = 10 - 4 = 6
Our second triangle side = 4 - -2 = 6
Using the slope we calculated
Tan(Angle1) = -1
Angle1 = Atan(-1)
Angle1 = -45°
Since we have a right triangle
We only have 90° left
Angle2 = 90 - -45° = 135
Calculate the y intercept of our line
The y intercept is found by
Setting x = 0 in y = -x + 8
y = -(0) + 8
y = 8
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) = (10,-2) + t(4 - 10,4 - -2)
(x,y) = (10,-2) + t(-6,6)
x = 10 - 6t
y = -2 + 6t
Calculate Symmetric Equations:
| x - x0 | |
| z |
| y - y0 |
| b |
Plugging in our numbers, we get:
| x - 10 | |
| -6 |
| y - -2 |
| 6 |
Plot these points on the Cartesian Graph:
Final Answers
Slope Intercept = y = -x + 8
Distance Between Points = 8.4853
Midpoint = (7, 1)
Angle 1 = -45
Angle 2 = 135
Y-intercept = 8
You have 2 free calculationss remaining
What is the Answer?
Slope Intercept = y = -x + 8
Distance Between Points = 8.4853
Midpoint = (7, 1)
Angle 1 = -45
Angle 2 = 135
Y-intercept = 8
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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