SLOPES
SLOPES
Slope of a line is rise over run, meaning vertical change divided by horizontal
change (moving from left to right in the usual coordinate system).
The equation of a line passing through a point (xo,yo) and having slope m
can be written (in so-called point-slope form)
y=m(x−xo)+yo or y−yo=m(x−xo)
The equation of the line passing through two points (x1,y1),(x2,y2) can be
written (in so-called two-point form) as
y −y
y= 1 2 (x−x1)+y1
௫1−x2
SLOPE
...unless x1=x2
, in which case the two points are aligned vertically, and the line can't be written that
way. Instead, the description of a vertical line through a point with horizontal coordinate
x1
is just
x=x1
Of course, the two‐point form can be derived from the point‐slope form, since the slope
m
of a line through two points (x1,y1),(x2,y2)
is that possibly irritating expression which occurs above:
y −y
m= x1−x2
1 2
EXAMPLE:
Write the equation for the line passing through the two points (1,2) and (3,8)
EXAMPLE:
Write the equation for the line passing through the point (1,2) with slope 3.