Equationsof Lines
LearningObjectives
- identifyand writeequationsin slope-interceptform.
- identifyequationsof parallellines.
- identifyequationsof perpendicularlines.
- identifyand writeequationsin standardform.
Introduction
Everyline that you can representgraphicallyon the coordinateplanecan also be representedalgebraically.
That meansthat you can createan equationrelating and that correspondsto any graphof a straight
line. In this lesson,you’lllearnhow to createan equationfrom a graphor pointsgiven,identifyequationsof
paralleland perpendicularlines,and practiceusingboth slope-interceptand standardform.
Slope-InterceptEquations
The first type of linearequationto studyis the moststraightforward.It is calledslope-interceptformand
involvesboth the slopeof the line and its -intercept.A -interceptis the pointat whichthe line crosses
the vertical axis. So, it will be the valueof when is equalto 0. The genericformulafor an equation
in slope-interceptform is as follows.
In this equation, and remainas variables, is the slopeof the line, and is the -interceptof the
line. So, if you knowthat a line has a slopeof 4 and it crossesthe -axisat its equationin slope-
interceptform wouldbe.
This form is especiallyusefulfor identifyingthe equationof a line givenits graph.You alreadyknowhow to
deducethe slopeby findingtwo pointsand usingthe slopeformula.You can identifythe -interceptby
sightby findingwherethe line crossesthe -axison the graph.The valueof is the -coordinateof this
point.
Example 1
Writean equationin slope-interceptform that representsthe followingline.