Line Equation-Slope-Distance-Midpoint-Y intercept Calculator ·

13 May 2024, 00:00

Given (1, 9) and (5, 3)

calculate 8 items:

Calculate the slope and point-slope form:

Slope (m) =	y2 - y1
	x2 - x1

Slope (m) =	3 - 9
	5 - 1

Slope (m) =	-6
	4

GCF Calculation

Reduce numerator and denominator by the (GCF) of 1

Slope = (-6/1)/(4/1)

Slope =	-6
	4

Calculate the point-slope form :

y - y1 = m(x - x1)

y - 9 = -3/2(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, 9) and the slope (m) = -3/2

b = 9 - (-3/2 * 1)

b = 9 - (-6/4)

b =	36
	4

b =	21
	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 21

Our reduced fraction is:

1
0.095238095238095

Build standard line equation

y = -3/2x + 1/0.095238095238095

Distance between the 2 points

D = Square Root((x2 - x1)2 + (y2 - y1)2)

D = Square Root((5 - 1)2 + (3 - 9)2)

D = Square Root((42 + -62))

D = √(16 + 36)

D = √52

D = 7.2111

Midpoint between the 2 points

Midpoint =

Midpoint =

Midpoint =

Midpoint = (3, 6)

Form a right triangle

Plot a 3rd point (5,3)

Our first triangle side = 5 - 1 = 4

Our second triangle side = 9 - 3 = 6

Using the slope we calculated
Tan(Angle1) = -1.5

Angle1 = Atan(-1.5)

Angle1 = -56.3099°

Since we have a right triangle
We only have 90° left
Angle2 = 90 - -56.3099° = 146.3099

Calculate the y intercept of our line

The y intercept is found by
Setting x = 0 in y = -3/2x + 1/0.095238095238095

y = -3/2(0) + 1/0.095238095238095

y = 1/0.095238095238095

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) = (1,9) + t(5 - 1,3 - 9)

(x,y) = (1,9) + t(4,-6)

x = 1 + 4t

y = 9 - 6t

Calculate Symmetric Equations:

Plugging in our numbers, we get:

Plot these points on the Cartesian Graph:

Final Answers

Slope = -6/4 or -1.5
Slope Intercept = y = -3/2x + 1/0.095238095238095
Distance Between Points = 7.2111
Midpoint = (3, 6)
Angle 1 = -56.3099
Angle 2 = 146.3099
Y-intercept = 1/0.095238095238095

You have 1 free calculations remaining

What is the Answer?

Slope = -6/4 or -1.5
Slope Intercept = y = -3/2x + 1/0.095238095238095
Distance Between Points = 7.2111
Midpoint = (3, 6)
Angle 1 = -56.3099
Angle 2 = 146.3099
Y-intercept = 1/0.095238095238095

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 time
d = 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

Line Equation-Slope-Distance-Midpoint-Y intercept Calculator

Given (1, 9) and (5, 3) calculate 8 items: Reduce numerator and denominator by the (GCF) of 1 Slope = (-6/1)/(4/1) y - y1 = m(x - x1) y - 9 = -3/2(x - 1) Standard equation of a line is y = mx + bwhere m is our slopex and y are points on