Line Equation-Slope-Distance-Midpoint-Y intercept Calculator
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Given (1, 3) and (0, 0)
calculate 8 items:
Calculate the slope and point-slope form:
Slope (m) =
y2 - y1
x2 - x1
Slope (m) =
0 - 3
0 - 1
Slope (m) =
-3
-1
Slope = 3
Calculate the point-slope form :
y - y1 = m(x - x1)
y - 3 = 3(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, 3) and the slope (m) = 3
b = 3 - (3 * 1)
b = 3 + 0
b =
3
1
Solve for b
b = -3/-1
Build standard line equation
y = 3x
Distance between the 2 points
D = Square Root((x2 - x1)2 + (y2 - y1)2)
D = Square Root((0 - 1)2 + (0 - 3)2)
D = Square Root((-12 + -32))
D = √(1 + 9)
D = √10
D = 3.1623
Midpoint between the 2 points
Midpoint =
x2 + x1
2
,
y2 + y1
2
Midpoint =
1 + 0
2
,
3 + 0
2
Midpoint =
1
2
,
3
2
Form a right triangle
Plot a 3rd point (1,0)
Our first triangle side = 1 - 0 = 1
Our second triangle side = 3 - 0 = 3
Using the slope we calculated Tan(Angle1) = 3
Angle1 = Atan(3)
Angle1 = 71.5651°
Since we have a right triangle We only have 90° left Angle2 = 90 - 71.5651° = 18.4349
Calculate the y intercept of our line
The y intercept is found by Setting x = 0 in y = 3x
y = 3(0)
y =
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) = (1,3) + t(0 - 1,0 - 3)
(x,y) = (1,3) + t(-1,-3)
x = 1 - t
y = 3 - 3t
Calculate Symmetric Equations:
x - x0
z
y - y0
b
Plugging in our numbers, we get:
x - 1
-1
y - 3
-3
Plot these points on the Cartesian Graph:
Final Answers
Slope = 0/-1 or 3 Slope Intercept = y = 3x Distance Between Points = 3.1623 Midpoint = (1/2, 3/2) Angle 1 = 71.5651 Angle 2 = 18.4349 Y-intercept =
You have 2 free calculationss remaining
What is the Answer?
Slope = 0/-1 or 3 Slope Intercept = y = 3x Distance Between Points = 3.1623 Midpoint = (1/2, 3/2) Angle 1 = 71.5651 Angle 2 = 18.4349 Y-intercept =
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