Chapter 5 The Straight Line Gradient of a Straight LineThegradientofastraightlineistheratioofthevertical distancetothehorizontal distancebetweenanytwogivenpointsonthestraightline.Gradient, m = Thegradient(m)ofastraightlineisdefinedtobe:Changeinverticalheight.Changeinhorizontaldistance.Usethisdefinitiontocalculatethegradientofvariousstraightlines:distance. horizontal in changeheight. vertical in changem =3indthegradientsofthestraightlinesbelow:(!)"3m# ""($)%"m# %"(3)""m# "m#!distance. horizontal in changeheight. vertical in changem =(&)'(m#('#3"(())3m#3)#3*egative+radientConsiderthestraightlinesshownbelow:(a) (c)(b)(d)(e)Canyousplitthelinesintotwogroupsbasedontheirgradients,-ines(a)(c)and(d)slopeupwardsfromlefttoright.-ines(b)and(e)slopedownwardsfromlefttoright..ositivegradient*egativegradientCalculatethegradientsofthelinesbelow:(!)/"&($)/'(54 = m3"(' == mThe01uationofa2traight-ine.Tofindthee1uationofanystraightlinewere1uireto3nowtwothings:(a)Thegradientoftheline.(b)Theya4isinterceptoftheline.m#gradient.c#ya4isintercept.Thee1uationofastraightlineis: y#m45c04amples.+ivethegradientandtheya4isinterceptforeachofthefollowinglines.(!)y#(45&m#( c#&($)y#"45$m#" c#$(3)y#4/3m#! c#/3indingThe01uation.indthee1uationofthestraightlinesbelow:4y(!)6hatisthegradient, m#!6hatistheya4isintercept, c#$*owusey#m45c y#45$4y($)c#!21m =121y + = x(3)4yc#/$(")4ym#/$c#3y#/$45323m =223y = x4y(&)c#((()4yc#$34m =634y + = x32m =232y + = xThe+radientormula.The+radientormula.-oo3atthediagrambelow:4!4$y!y$7tshowsastraightlinepassingthroughthepoints(4!8y!)and(4$8y$).6emustcalculatethegradientofthelineusingthetriangleshown:Changeinverticalheight:y$/y!y$9y!Changeinhorizontaldistance:4$/4!4$/4!+radientofline:1 21 2 y ym=Calculatethegradientofthelinethroughthepointsbelow:(!):("8()and;(!