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

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

Given the two points you entered of (-4, 5) and (7, -3), we need to calculate 8 items:

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

Slope (m) = | -3 - 5 |

7 - -4 |

Slope (m) = | -8 |

11 |

y - y

y - 5 = -8/11(x + 4)

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 = (-4, 5) and the slope (m) = -8/11 that we calculated, let's plug in those values and evaluate:

b = 5 - (-8/11 * -4)

b = 5 - (32/11)

b = | 55 |

11 |

- |

32 |

11 |

b = | 23 |

11 |

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 | |

0.22 |

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

y = -8/11x + 1/0.22

Distance = Square Root((x

Distance = Square Root((7 - -4)

Distance = Square Root((11

Distance = √(121 + 64)

Distance = √185

Distance = 13.6015

Midpoint = |

x_{2} + x_{1} |

2 |

, |

y_{2} + y_{1} |

2 |

Midpoint = | |

-4 + 7 |

2 |

, |

5 + -3 |

2 |

Midpoint = | |

3 |

2 |

, |

2 |

2 |

Midpoint = (3/2, 1)

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

Our first triangle side = 7 - -4 = 11

Our second triangle side = 5 - -3 = 8

Using the slope we calculated, Tan(Angle1) = -0.73

Angle1 = Atan(-0.73)

Angle1 = -36.0274°

Since we have a right triangle, we only have 90 degrees left, so Angle2 = 90 - -36.0274° = 126.0274

The y intercept is found by setting x = 0 in the line equation y = -8/11x + 1/0.22

y = -8/11(0) + 1/0.22

y =

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

(x,y) = (-4,5) + t(7 - -4,-3 - 5)

(x,y) = (-4,5) + t(11,-8)

x - x_{0} | |

z |

y - y_{0} |

b |

x - -4 | |

11 |

y - 5 |

-8 |

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