Given (0, 20) and (12, 30)

calculate 8 items:

##### Calculate the slope and point-slope form:

Slope (m)= | y2 - y1 |

x2 - x1 |

Slope (m)= | 30 - 20 |

12 - 0 |

Slope (m)= | 10 |

12 |

##### GCF Calculation

Reduce numerator and denominator by the (GCF) of 10

Slope = (10/10)/(12/10)

Slope= | 1 |

1.2 |

##### Calculate the point-slope form :

y - y1 = m(x - x1)

y - 20 = 5/6(x - 0)

##### 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 (0, 20) and the slope (m) = 5/6

b = 20 - (5/6 * 0)

b = 20 - (0/1.2)

b= | 24 |

1.2 |

b= | 120 |

6 |

##### 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 120

Our reduced fraction is:

##### Build standard line equation

y = 5/6x + 20

##### Distance between the 2 points

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

D = Square Root((12 - 0)2 + (30 - 20)2)

D = Square Root((122 + 102))

D = √(144 + 100)

D = √244

D = 15.6205

##### Midpoint between the 2 points

Midpoint = |

Midpoint = | |

Midpoint = | |

Midpoint = (6, 25)

##### Form a right triangle

Plot a 3rd point (12,20)

Our first triangle side = 12 - 0 = 12

Our second triangle side = 30 - 20 = 10

Using the slope we calculated

Tan(Angle1) = 0.83333333333333

Angle1 = Atan(0.83333333333333)

Angle1 = 39.8056°

Since we have a right triangle

We only have 90° left

Angle2 = 90 - 39.8056° = 50.1944

##### Calculate the y intercept of our line

The y intercept is found by

Setting x = 0 in y = 5/6x + 20

y = 5/6(0) + 20

y = **20**

##### 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) = (0,20) + t(12 - 0,30 - 20)

(x,y) = (0,20) + t(12,10)

**x = 0 + 12t**

**y = 20 + 10t**

##### Calculate Symmetric Equations:

##### Plugging in our numbers, we get:

##### Plot these points on the Cartesian Graph:

##### Final Answers

Slope = 1/1.2 or 0.83333333333333

Slope Intercept = y = 5/6x + 20

Distance Between Points = 15.6205

Midpoint = (6, 25)

Angle 1 = 39.8056

Angle 2 = 50.1944

Y-intercept = 20

*You have 1 free calculations remaining*

##### What is the Answer?

Slope = 1/1.2 or 0.83333333333333

Slope Intercept = y = 5/6x + 20

Distance Between Points = 15.6205

Midpoint = (6, 25)

Angle 1 = 39.8056

Angle 2 = 50.1944

Y-intercept = 20

##### 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

##### Example calculations for the Line Equation-Slope-Distance-Midpoint-Y intercept Calculator

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

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