Line Equation-Slope-Distance-Midpoint-Y intercept Calculator
Given (1, 4) and (2, 6) calculate 8 items:
Calculate the slope and point-slope form:
Slope (m) =
y2 - y1
x2 - x1
Slope (m) =
6 - 4
2 - 1
Slope (m) =
2
1
Slope = 2
Calculate the point-slope form :
y - y1 = m(x - x1) y - 4 = 2(x - 1)
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 (1, 4) and the slope (m) = 2 b = 4 - (2 * 1) b = 4 + 2
b =
2
1
Solve for b
b = 2
Build standard line equation
y = 2x + 2
Distance between the 2 points
D = Square Root((x2 - x1)2 + (y2 - y1)2) D = Square Root((2 - 1)2 + (6 - 4)2) D = Square Root((12 + 22)) D = √(1 + 4) D = √5 D = 2.2361
Midpoint between the 2 points
Midpoint =
x2 + x1
2
,
y2 + y1
2
Midpoint =
1 + 2
2
,
4 + 6
2
Midpoint =
3
2
,
10
2
Midpoint = (3/2, 5)
Form a right triangle
Plot a 3rd point (2,4) Our first triangle side = 2 - 1 = 1 Our second triangle side = 6 - 4 = 2
Using the slope we calculated Tan(Angle1) = 2 Angle1 = Atan(2) Angle1 = 63.4349° Since we have a right triangle We only have 90° left Angle2 = 90 - 63.4349° = 26.5651
Calculate the y intercept of our line
The y intercept is found by Setting x = 0 in y = 2x + 2 y = 2(0) + 2 y = 2
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) = (1,4) + t(2 - 1,6 - 4) (x,y) = (1,4) + t(1,2) x = 1 + t y = 4 + 2t
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)
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
