Point 1: (x_{1} =
_{1} =

Point 2: (x_{2} =
_{2} =

Given the two points you entered of (1, 4) and (5, 6), we need to calculate 8 items:

Slope (m) = y _{2}- y_{1}x _{2}- x_{1}

Slope (m) = | 6 - 4 |

5 - 1 |

Slope (m) = | 2 |

4 |

Since the slope is not fully reduced, we reduce numerator and denominator by the (GCF) of 2

Slope = (2/2)/(4/2)

Slope = 1/2

y - y

y - 4 = 1/2(x - 1)

The standard equation of a line is y = mx + b where m is our slope, x and y are points on the line, and b is a constant.

Rearranging that equation to solve for b, we get b = y - mx. Using the first point that you entered = (1, 4) and the slope (m) = 1/2 that we calculated, let's plug in those values and evaluate:

b = 4 - (1/2 * 1)

b = 4 - (1/2)

b = | 8 |

2 |

- |

1 |

2 |

b = | 7 |

2 |

This fraction is not reduced. Using our GCF Calculator, we see that the top and bottom of the fraction can be reduced by 7

Our reduced fraction is:

1 | |

0.29 |

Now that we have calculated (m) and (b), we have the items we need for our standard line equation:

y = 1/2x + 1/0.29

Distance = Square Root((x

Distance = Square Root((5 - 1)

Distance = Square Root((4

Distance = √(16 + 4)

Distance = √20

Distance = 4.4721

Midpoint = |

x_{2} + x_{1} |

2 |

, |

y_{2} + y_{1} |

2 |

Midpoint = | |

1 + 5 |

2 |

, |

4 + 6 |

2 |

Midpoint = | |

6 |

2 |

, |

10 |

2 |

Midpoint = (3, 5)

Using our 2 points, we form a right triangle by plotting a 3

Our first triangle side = 5 - 1 = 4

Our second triangle side = 6 - 4 = 2

Using the slope we calculated, Tan(Angle1) = 0.5

Angle1 = Atan(0.5)

Angle1 = 26.5651°

Since we have a right triangle, we only have 90 degrees left, so Angle2 = 90 - 26.5651° = 63.4349

The y intercept is found by setting x = 0 in the line equation y = 1/2x + 1/0.29

y = 1/2(0) + 1/0.29

y =

Parametric equations are written in the form (x,y) = (x_{0},y_{0}) + t(b,-a)

(x,y) = (1,4) + t(5 - 1,6 - 4)

(x,y) = (1,4) + t(4,2)

x - x_{0} | |

z |

y - y_{0} |

b |

x - 1 | |

4 |

y - 4 |

2 |

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