Given (4, 4) and (0, 6)
calculate 8 items:
Calculate the slope and point-slope form:
| Slope (m) = | y2 - y1 |
| x2 - x1 |
| Slope (m) = | 6 - 4 |
| 0 - 4 |
| Slope (m) = | 2 |
| -4 |
GCF Calculation
Reduce numerator and denominator by the (GCF) of 2
Slope = (2/2)/(-4/2)
| Slope = | 1 |
| -2 |
Calculate the point-slope form :
y - y1 = m(x - x1)
y - 4 = -1/2(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, 4) and the slope (m) = -1/2
b = 4 - (-1/2 * 4)
b = 4 - (4/-2)
| b = | -8 |
| -2 |
| b = | 12 |
| 2 |
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 12
Our reduced fraction is:
| 1 | |
| 0.16666666666667 |
Build standard line equation
y = -1/2x + 6
Distance between the 2 points
D = Square Root((x2 - x1)2 + (y2 - y1)2)
D = Square Root((0 - 4)2 + (6 - 4)2)
D = Square Root((-42 + 22))
D = √(16 + 4)
D = √20
D = 4.4721
Midpoint between the 2 points
| Midpoint = |
| Midpoint = | |
| Midpoint = | |
Midpoint = (2, 5)
Form a right triangle
Plot a 3rd point (4,4)
Our first triangle side = 4 - 0 = 4
Our second triangle side = 6 - 4 = 2
Using the slope we calculated
Tan(Angle1) = -0.5
Angle1 = Atan(-0.5)
Angle1 = -26.5651°
Since we have a right triangle
We only have 90° left
Angle2 = 90 - -26.5651° = 116.5651
Calculate the y intercept of our line
The y intercept is found by
Setting x = 0 in y = -1/2x + 6
y = -1/2(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) = (4,4) + t(0 - 4,6 - 4)
(x,y) = (4,4) + t(-4,2)
x = 4 - 4t
y = 4 + 2t
Calculate Symmetric Equations:
Plugging in our numbers, we get:
Plot these points on the Cartesian Graph:
Final Answers
Slope = 1/-2 or -0.5
Slope Intercept = y = -1/2x + 6
Distance Between Points = 4.4721
Midpoint = (2, 5)
Angle 1 = -26.5651
Angle 2 = 116.5651
Y-intercept = 6
What is the Answer?
Slope = 1/-2 or -0.5
Slope Intercept = y = -1/2x + 6
Distance Between Points = 4.4721
Midpoint = (2, 5)
Angle 1 = -26.5651
Angle 2 = 116.5651
Y-intercept = 6
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 timed = 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
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