Line Equation-Slope-Distance-Midpoint-Y intercept Calculator
Given (-4, 5) and (7, -3) calculate 8 items:
Calculate the slope and point-slope form:
Slope (m) =
y2 - y1
x2 - x1
Slope (m) =
-3 - 5
7 - -4
Slope (m) =
-8
11
Calculate the point-slope form :
y - y1 = m(x - x1) y - 5 = -8/11(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, 5) and the slope (m) = -8/11 b = 5 - (-8/11 * -4) b = 5 - (32/11)
b =
55
11
-
32
11
b =
23
11
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 23 Our reduced fraction is:
1
0.47826086956522
Build standard line equation
y = -8/11x + 1/0.47826086956522
Distance between the 2 points
D = Square Root((x2 - x1)2 + (y2 - y1)2) D = Square Root((7 - -4)2 + (-3 - 5)2) D = Square Root((112 + -82)) D = √(121 + 64) D = √185 D = 13.6015
Midpoint between the 2 points
Midpoint =
x2 + x1
2
,
y2 + y1
2
Midpoint =
-4 + 7
2
,
5 + -3
2
Midpoint =
3
2
,
2
2
Midpoint = (3/2, 1)
Form a right triangle
Plot a 3rd point (7,-3) Our first triangle side = 7 - -4 = 11 Our second triangle side = 5 - -3 = 8
Using the slope we calculated Tan(Angle1) = -0.72727272727273 Angle1 = Atan(-0.72727272727273) Angle1 = -36.0274° Since we have a right triangle We only have 90° left Angle2 = 90 - -36.0274° = 126.0274
Calculate the y intercept of our line
The y intercept is found by Setting x = 0 in y = -8/11x + 1/0.47826086956522 y = -8/11(0) + 1/0.47826086956522 y = 1/0.47826086956522
Find the parametric equations for the line
Parametric equations are written as (x,y) = (x0,y0) + t(b,-a)
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
