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Slopes Of Lines

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Updated 2009-02-28 17:18

Slopes of Lines

EquationsProperties
y-y1=m(x-x1)Line with slope m passing through the point (x1, y1).
y=mx+bLine with slope m,
x-intercept -b/m, and y-intercept b.
Ax+By=CLine with slope -A/B,
x-intercept C/A, and y-intercept C/B.
(y2-y1)/(x2-x1)Slope m of line through the points (x1, y1) and (x2, y2).
rise/runSlope of a line.
y=mx+b and y=mx+cTwo parallel lines.
y=mx+b and y=-(x/m)+cTwo perpendicular lines.
Ax+By=C and Ax+By=DTwo parallel lines.
Ax+By=C and Bx-Ay=DTwo perpendicular lines.
y=mx+b with m>0A line with y that rises as x rises.
y=mx+b with m<0A line with y that falls as x rises.
(x,y) with x=(x1+x2)/2
        and y=(y1+y2)/2
Midpoint of segment connecting the points
(x1,y1) and (x2,y2)
sqrt[(x1-x2)2+(y1-y2)2]Length of segment connecting the points
(x1,y1) and (x2,y2)
sqrt[(x1-x2)2+(y1-y2)2]Distance between the points
(x1,y1) and (x2,y2)
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EquationsProperties
y=-3x+2Line with slope -3 and y-intercept +2.
y=3x-2Line with slope +3 and y-intercept -2.
y=-2x+3Line with slope -2 and y-intercept +3.
y=2x-3Line with slope +2 and y-intercept -3.
y=3Horizontal line with y-intercept +3.
y=-2Line with zero slope and y-intercept -2.
x=2Vertical line with x-intercept +2.
x=-3Line with undefined slope and x-intercept -3.
y=3x+2Line with slope +3 and x-intercept -2/3.
y=2x+3Line with slope +2 and x-intercept -3/2.
3x+2y=0Line with slope -3/2 passing through origin.
3x+2y=6Line with slope -3/2 passing through (1,3/2).
2x-3y=0Line with slope +2/3 passing through origin.
2x-3y=6Line 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+5Line passing through (2,3) and (3,2).
y=x+5Line passing through (-3,2) and (-2,3).
x-5y=13Line passing through (3,-2) and (-2,-3).
5x+y=13Line passing through (3,-2) and (2,3).
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EquationsProperties
3y-6x=9Line identical to y=2x+3.
y=-(x/3)+2Line identical to x+3y=6.
y=x+20Line parallel to y=x+5.
8x-2y=3Line parallel to 8x-2y=5.
x+y=6Line parallel to y=-x+5.
y=-4x+10Line parallel to 8x+2y=5.
y=(x/2)+5Line perpendicular to y=-2x+3.
x+2y=4 Line perpendicular to y=2x+3.
3x+y=2Line perpendicular to x-3y=5.
y=3x+6Line 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).
10Length of segment connecting (-3,2) to (5,-4).
13Length of segment connecting (-3,-4) to (9,1).
17Distance between the points (12,-7) and (4,8).
25Distance between the points (-15,6) and (9,13).
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EquationsProperties
5x+3y=6 and 2x+3y=3Two lines that cross only at (1,1/3).
5x+3y=6 and 5x+3y=3Two parallel lines that never cross.
2x+3y=3 and 4x+6y=6Two identical lines.
2x+3y=4 and 3x-2y=6Two perpendicular lines that cross only at (2,0).
y=3x+4 and y=2x+3Two lines that cross only at (-1,1).
y=3x+4 and y=3x+5Two parallel lines that never cross.
y=-(x/3)+5 and y=3x+5Two perpendicular lines that cross only at (0,5).
x=4 and y=3Two perpendicular lines that cross only at (4,3).
x=2 and x=5Two vertical parallel lines that never cross.
y=-3 and y=-2Two horizontal parallel lines that never cross.
x=4 and y=x+3Two lines that cross only at (4,7).
y=5 and 2x+3y=7Two lines that cross only at (-4,5).
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