- Plot a line on a coordinateplaneusingdifferentmethods.
Introduction
You may recallfrom algebrathat you spenta lot of time graphinglinesin the -coordinateplane.How
are thoselinesrelatedto the lineswe’vestudiedin geometry?Lineson a graphcan be studiedfor their
slope(or rate of change),and how they intersectthe - and -axes.
Slopein the CoordinatePlane
If you look at a graphof a line, you can thinkof the slopeas the steepnessof the line (assumingthat the
- and - scalesare equal.Mathematically, you can calculatethe slopeusingtwo differentpointson a line.
Giventwo points and the slopeis computedas:
You may havealso learnedthis as “slopeequalsrise over run.”In otherwords,first calculatethe distance
that the line travelsup (or down),and then dividethat valueby the distancethe line travelsleft to right.The
left to right distancein this scenariois referredto as the run.
A line that goesup from left to right has positiveslope,and a line that goesdownfrom left to right has neg-
ativeslope.
Example 1
Whatis the slopeof a line that travelsthroughthe points(2, 2) and (4, 6)?You can use the previousformulato find the slopeof this line. Let’s say that is (2, 2) and
is (4, 6). Thenwe find the slopeas follows:
The slopeof the line in Example1 is 2. Let’s look at whatthat meansgraphically.