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# Slopes Of Lines

rename
Updated
2009-02-28 17:18

## Slopes of Lines

Equations | Properties |
---|---|

y-y_{1}=m(x-x_{1}) | Line with slope m passing through the point (x_{1}, y_{1}). |

y=mx+b | Line with slope m, x-intercept -b/m, and y-intercept b. |

Ax+By=C | Line with slope -A/B, x-intercept C/A, and y-intercept C/B. |

(y_{2}-y_{1})/(x_{2}-x_{1}) | Slope m of line through the points (x_{1}, y_{1}) and (x_{2}, y_{2}). |

rise/run | Slope of a line. |

y=mx+b and y=mx+c | Two parallel lines. |

y=mx+b and y=-(x/m)+c | Two perpendicular lines. |

Ax+By=C and Ax+By=D | Two parallel lines. |

Ax+By=C and Bx-Ay=D | Two perpendicular lines. |

y=mx+b with m>0 | A line with y that rises as x rises. |

y=mx+b with m<0 | A line with y that falls as x rises. |

(x,y) with x=(x_{1}+x_{2})/2and y=(y _{1}+y_{2})/2 | Midpoint of segment connecting the points (x _{1},y_{1}) and (x_{2},y_{2}) |

sqrt[(x_{1}-x_{2})^{2}+(y_{1}-y_{2})^{2}] | Length of segment connecting the points (x _{1},y_{1}) and (x_{2},y_{2}) |

sqrt[(x_{1}-x_{2})^{2}+(y_{1}-y_{2})^{2}] | Distance between the points (x _{1},y_{1}) and (x_{2},y_{2}) |

Equations | Properties |
---|---|

y=-3x+2 | Line with slope -3 and y-intercept +2. |

y=3x-2 | Line with slope +3 and y-intercept -2. |

y=-2x+3 | Line with slope -2 and y-intercept +3. |

y=2x-3 | Line with slope +2 and y-intercept -3. |

y=3 | Horizontal line with y-intercept +3. |

y=-2 | Line with zero slope and y-intercept -2. |

x=2 | Vertical line with x-intercept +2. |

x=-3 | Line with undefined slope and x-intercept -3. |

y=3x+2 | Line with slope +3 and x-intercept -2/3. |

y=2x+3 | Line with slope +2 and x-intercept -3/2. |

3x+2y=0 | Line with slope -3/2 passing through origin. |

3x+2y=6 | Line with slope -3/2 passing through (1,3/2). |

2x-3y=0 | Line with slope +2/3 passing through origin. |

2x-3y=6 | Line with slope +2/3 passing through (3/2,-1). |

y-2=(3/2)(x-3) | Line with slope +3/2 passing through (3,2). |

y+3=(-2/3)(x+2) | Line with slope -2/3 passing through (-2,-3). |

y=-x+5 | Line passing through (2,3) and (3,2). |

y=x+5 | Line passing through (-3,2) and (-2,3). |

x-5y=13 | Line passing through (3,-2) and (-2,-3). |

5x+y=13 | Line passing through (3,-2) and (2,3). |

Equations | Properties |
---|---|

3y-6x=9 | Line identical to y=2x+3. |

y=-(x/3)+2 | Line identical to x+3y=6. |

y=x+20 | Line parallel to y=x+5. |

8x-2y=3 | Line parallel to 8x-2y=5. |

x+y=6 | Line parallel to y=-x+5. |

y=-4x+10 | Line parallel to 8x+2y=5. |

y=(x/2)+5 | Line perpendicular to y=-2x+3. |

x+2y=4 | Line perpendicular to y=2x+3. |

3x+y=2 | Line perpendicular to x-3y=5. |

y=3x+6 | Line perpendicular to x+3y=6. |

(x,y)=(5,-3) | Midpoint of segment connecting (-7,10) to (17,-16). |

(x,y)=(-2,7) | Midpoint of segment connecting (-13,-8) to (9,22). |

(x,y)=(-8,-1) | Midpoint of segment connecting (-1,-19) to (-15,17). |

(x,y)=(9,4) | Midpoint of segment connecting (17,-9) to (1,17). |

10 | Length of segment connecting (-3,2) to (5,-4). |

13 | Length of segment connecting (-3,-4) to (9,1). |

17 | Distance between the points (12,-7) and (4,8). |

25 | Distance between the points (-15,6) and (9,13). |

Equations | Properties |
---|---|

5x+3y=6 and 2x+3y=3 | Two lines that cross only at (1,1/3). |

5x+3y=6 and 5x+3y=3 | Two parallel lines that never cross. |

2x+3y=3 and 4x+6y=6 | Two identical lines. |

2x+3y=4 and 3x-2y=6 | Two perpendicular lines that cross only at (2,0). |

y=3x+4 and y=2x+3 | Two lines that cross only at (-1,1). |

y=3x+4 and y=3x+5 | Two parallel lines that never cross. |

y=-(x/3)+5 and y=3x+5 | Two perpendicular lines that cross only at (0,5). |

x=4 and y=3 | Two perpendicular lines that cross only at (4,3). |

x=2 and x=5 | Two vertical parallel lines that never cross. |

y=-3 and y=-2 | Two horizontal parallel lines that never cross. |

x=4 and y=x+3 | Two lines that cross only at (4,7). |

y=5 and 2x+3y=7 | Two lines that cross only at (-4,5). |