Write an equation in point-slope form for the line through the given point with the given

slope.

1. (10, –9); m = −2

2. (9, –8); m = 5/6

3. (10, 6); m = -2/3

4. (7, 10); m = - 1/2

5. (–1, 2); m = 1

6. A line passes through (2, –1) and (8, 4). Write an equation for the line in point-slope form.

7. A line passes through (4, 3) and (10, 10). Write an equation for the line in point-slope form.

8. A line passes through (–5, –9) and (2, –6). Write an equation for the line in point-slope form.

9. A line passes through (–1, 3) and (10, 9). Write an equation for the line in point-slope form.

10. A line passes through (–7, –3) and (4, 4). Write an equation for the line in point-slope form.

Is the relationship shown by the data linear? If so, model the data with an equation.

11.

X | Y |

–9 | -2 |

-5 | -7 |

-1 | -12 |

3 | -17 |

12.

X | Y |

9 | 1 |

15 | 3 |

21 | 5 |

27 | 7 |

13.

X | Y |

-9 | -3 |

-3 | -2 |

3 | 0 |

9 | 1 |

14.

X | Y |

5 | -2 |

11 | -1 |

17 | 0 |

23 | 1 |

15.

X | Y |

-5 | 1 |

-1 | 0 |

3 | -1 |

7 | -2 |

HaleyWoodall17 Sep 17, 2015

#4**+10 **

6. A line passes through (2, –1) and (8, 4). Write an equation for the line in point-slope form.

( x1, y1) (x2 , y2)

Use the above to find the slope, m, which is given by :

m = [ y2 - y1] / [ x2 - x1] = [4 - (-1)] / [ 8 - 2) = 5/6

Then..... just use * one *of the points (either one, doesn't matter) and do what we just did in 1 -5

y - 4 = (5/6)(x - 8)

This example should get you through number 10

I'll finish the rest in a little while

CPhill Sep 17, 2015

#2**+10 **

Sorry, Haley.....they wanted point-slope form....here we go

These examples should cover every problem 3 - 5.......

Point-slope form .......y - y_{1} = m(x - x_{1})

1. (10, –9); m = −2 → y - (-9)= -2(x - 10)

2. (9, –8); m = 5/6 → y - (-8) = (5/6) (x - 9)

CPhill Sep 17, 2015

#4**+10 **

Best Answer

6. A line passes through (2, –1) and (8, 4). Write an equation for the line in point-slope form.

( x1, y1) (x2 , y2)

Use the above to find the slope, m, which is given by :

m = [ y2 - y1] / [ x2 - x1] = [4 - (-1)] / [ 8 - 2) = 5/6

Then..... just use * one *of the points (either one, doesn't matter) and do what we just did in 1 -5

y - 4 = (5/6)(x - 8)

This example should get you through number 10

I'll finish the rest in a little while

CPhill Sep 17, 2015

#6**+10 **

11.

X Y

–9 -2

-5 -7

-1 -12

3 -17

OK Haley ....this isn't difficult....just time consuming

If the differences in the x's and y's are constant, we have a line....if not, we don't

Notice that the difference in one x to another reading downward is +4

For example -9 + 4 = -5 and -5 + 4 = -1 and -1 + 4 = 3 ...... etc.

And the difference in one y to another reading downward is also constant = -5

For example -2 - 5 = -7 and -7 - 5 = -12 ........etc

So...if we have a line......as we did in number 6.....use **any****two** of the points to find the slope and then write the equation

For exampe in 11, we can use ( -9, -2) and (-5, -7)

( x1, y1 ) (x2, y2)

The slope = m = [y2 - y1] / [ x2 - x1] = [-7 - (-2)] / [-5 - (-9)] = -5 / 4

And the equation .....in point-slope form is

y - (-7) = (-5/4) [ x - (-5)] [remember that we can use any point on the line in this equation]

The rest are similar.........if the differences in x's and y's are * not *constant......we don't have a line so don't worry about writing an equation in that case

[13 is not a line...the y's are not constant......don't worry about it....!!! ]

CPhill Sep 17, 2015