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! EquationofaLine Videos191,194,195onwww.corbettmaths.com Workout Question1: Writedownthegradientofeachoftheselines. (a)y=3x+1 (e)y=x−2 (b)y=2x−5 (c)y=7x+4 (d)y=10x+5 (f)y=6x (g)y=−4x+3 (h)y=−3x−7 (i) (j) Question2: Writedownwhereeachoftheselinescrossthey-axis(y-intercept) (a)y=2x+3 (b)y=7x+1 (c)y=3x−2 (d)y=x−5 (e)y=2x (f)y=−4x+6 (g)y=−5x−3 (h)y=−3x (i) (j) Question3: Writedowntheequationofthelinesbelow (a) gradientof3andy−interceptof6 (b)gradientof2andy−interceptof−1 (c)gradientof−4andy−interceptof3 (d)gradientof8andy−interceptof4 (e)gradientof1andpassingthough(0,4) (f)passingthrough(0,−2)withgradient4 (g)gradientof−5andpassingthroughtheorigin. Question4: (a)Doesthepoint(2,5)lieontheliney=3x−1? (b)Doesthepoint(4,1)lieontheliney=3x+1? (c)Doesthepoint(3,1)lieontheliney=x−3? (d)Doesthepoint(5,7)lieontheliney=−3x+22? (e)Doesthepoint(−4,−8)lieontheliney=−2x? (f)Doesthepoint(−1,8)lieontheliney=2x+11? (g)Doesthepoint(12,60)lieontheliney=7x−18? © CORBETTMATHS 2016 ! EquationofaLine Videos191,194,195onwww.corbettmaths.com Question5: Findtheequationofeachline (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k) (l) © CORBETTMATHS 2016 ! EquationofaLine Videos191,194,195onwww.corbettmaths.com Question6: Findtheequationofeachlinebelow. (a) (b) (c) (d) (f) (e) Question7: Findtheequationofthestraightlinethatpassesthroughthepoints (a)(0,3)and(4,19) (b)(0,2)and(6,20) (c)(0,0)and(1,4) (d)(0,−9)and(9,0) (e)(0,−6)and(7,8) (f)(−8,−10)and(0,14) (g)(0,2)and(10,7) (h)(−4,1)and(0,7) (i)(−4,0)and(0,18) Question8: Findtheequationofthestraightlinethat: (a)hasagradientof4andpassesthroughthepoint(1,10) (b)hasagradientof2andpassesthroughthepoint(−3,3) (c)hasagradientof1andpassesthroughthepoint(5,2) (d)hasagradientof−3andpassesthroughthepoint(−2,8) (e)hasagradientof−5andpassesthroughthepoint(3,−1) (f)hasagradientof½andpassesthroughthepoint(4,5) (g)hasagradientof⅖andpassesthroughthepoint(−5,−5) (h)hasagradientof−⅔andpassesthroughthepoint(9,15) © CORBETTMATHS 2016 ! EquationofaLine Videos191,194,195onwww.corbettmaths.com Question9: Findtheequationsofthelinesbelow (a) (b) (c) (e) (f) (d) Question10: Findtheequationofthestraightlinethatpassesthroughthesepairsofpoints (a)(2,5)and(4,11) (b)(−4,2)and(1,7) (c)(−5,−8)and(−4,−4) (d)(−1,−2)and(−6,3) (e)(−6,−4)and(−3,2) (f)(3,5)and(4,1) (g)(−5,4)and(5,2) (h)(1,6)and(5,4) (i)(−10,−5)and(−7,4) Question11: Findthecoordinateswherethefollowinglinescrossthex-axis (a)y=2x+6 (b)y=−x+4 (c)y=3x+9 (d)y=x−5 (e)y=4x+1 (f)y=−2x+10 (g)y=−4x−10 (h)y=5x+3 (i)y=½x+3 (j)x+y=8 (k)4x+2y+7=0 (l)3x+2y−8=0 Question12: Findthegradientsandthey-interceptsofeachoftheselines (a)x+y=10 (b)x−y=4 (d)3x−y=−1 (e)8x+2y+9=0 (f)5x−2y−4=0 (g)7x=1−2y (h)15y−6x=8 (i)⅔x+2y=5 (j)⅕y−½x=1 (k)⅔x+¾y=1½ © CORBETTMATHS 2016 (c)2x+y=6 ! EquationofaLine Videos191,194,195onwww.corbettmaths.com Apply Question1: Thepoint(5,−2)liesonwhichlinesbelow Question2: Dothepoints(1,4),(4,10)and(9,20)lieinastraightline? Question3: Alinehasequationy=2x+6 Thelinecrossesthex−axisatthepointA Thelinecrossesthey−axisatthepointB ThepointChascoordinates(1,8) Question4: (a)FindthecoordinatesofthepointA (b)FindthecoordinatesofthepointB (c)FindtheequationofthestraightlinepassingthroughthepointsAandC. Dothelinesy=3x+1and4x−2y+3=0havethesamegradients? Question5: Line1hasequationy=3x−12 (a)FindthecoordinatesofP (b)FindtheequationofLine2 Question6: Lexisaysthelinebelowhasan equationofy=−2x+8 Explainhermistake. © CORBETTMATHS 2016